In this paper,we give an explicit and systematic study on the double constructions of Frobenius Hom-algebras and introduce the close relations between O-operators and Homdendriform algebras.Furthermore,we study the do...In this paper,we give an explicit and systematic study on the double constructions of Frobenius Hom-algebras and introduce the close relations between O-operators and Homdendriform algebras.Furthermore,we study the double constructions of Connes cocycles in terms of Hom-dendriform algebras.Finally,we give a clear analogy between antisymmetric infinitesimal Hom-bialgebras and Hom-dendriform D-bialgebras.展开更多
In this paper,we study the Hom-structures of a special class of solvable Lie algebras with naturally graded filiform nilradical n_(n,1).Over an algebraically closed field F of zero characteristic,we calculate the Hom-...In this paper,we study the Hom-structures of a special class of solvable Lie algebras with naturally graded filiform nilradical n_(n,1).Over an algebraically closed field F of zero characteristic,we calculate the Hom-structures of these solvable Lie algebras using the Hom-Jacobi identity,obtain the bases of these Hom-structures and observe that there are certain similarities among these bases.展开更多
Semenov-Tian-Shansky has given the solution of the modified classical Yang-Baxter equation, which was called the modified r-matrix. Relevant studies have been extensive in recent times. In this paper, we introduce the...Semenov-Tian-Shansky has given the solution of the modified classical Yang-Baxter equation, which was called the modified r-matrix. Relevant studies have been extensive in recent times. In this paper, we introduce the concept and representations of modified RotaBaxter Hom-Lie algebras. We develop a cohomology of modified Rota-Baxter Hom-Lie algebras with coefficients in a suitable representation. As applications, we study formal deformations and abelian extensions of modified Rota-Baxter Hom-Lie algebras in terms of second cohomology groups.展开更多
Let F be a field of characteristic not 2, and let A be a finite-dimensional semisimple F -algebra. All local automorphisms of A are characterized when all the degrees of A are larger than 1. If F is further assumed to...Let F be a field of characteristic not 2, and let A be a finite-dimensional semisimple F -algebra. All local automorphisms of A are characterized when all the degrees of A are larger than 1. If F is further assumed to be an algebraically closed field of characteristic zero, K a finite group, F K the group algebra of K over F , then all local automorphisms of F K are also characterized.展开更多
In this paper,we show that an ideal generated by matching Rota-Baxter equations is a bideal of a Hopf algebra on decorated rooted forests.We then get a bialgebraic structure on the space of decorated rooted forests mo...In this paper,we show that an ideal generated by matching Rota-Baxter equations is a bideal of a Hopf algebra on decorated rooted forests.We then get a bialgebraic structure on the space of decorated rooted forests modulo this biideal.As an application,a connected graded bialgebra and so a graded Hopf algebra on matching Rota-Baxter algebras are constructed,which simplifies the Hopf algebraic structure proposed by[Pacific J.Math.,2022,317(2):441-475].展开更多
The modifiedλ-differential Lie-Yamaguti algebras are considered,in which a modifiedλ-differential Lie-Yamaguti algebra consisting of a Lie-Yamaguti algebra and a modifiedλ-differential operator.First we introduce t...The modifiedλ-differential Lie-Yamaguti algebras are considered,in which a modifiedλ-differential Lie-Yamaguti algebra consisting of a Lie-Yamaguti algebra and a modifiedλ-differential operator.First we introduce the representation of modifiedλ-differential Lie-Yamaguti algebras.Furthermore,we establish the cohomology of a modifiedλ-differential Lie-Yamaguti algebra with coefficients in a representation.Finally,we investigate the one-parameter formal deformations and Abelian extensions of modifiedλ-differential Lie-Yamaguti algebras using the second cohomology group.展开更多
A left Leibniz algebra equipped with an invariant nondegenerate skew-symmetric bilinear form(i.e.,a skew-symmetric quadratic Leibniz algebra)is constructed.The notion of T^(*)-extension of Lie-Yamaguti algebras is int...A left Leibniz algebra equipped with an invariant nondegenerate skew-symmetric bilinear form(i.e.,a skew-symmetric quadratic Leibniz algebra)is constructed.The notion of T^(*)-extension of Lie-Yamaguti algebras is introduced and it is observed that the trivial extension of a Lie-Yamaguti algebra is a quadratic Lie-Yamaguti algebra.It is proved that every symmetric(resp.,skew-symmetric)quadratic Leibniz algebra induces a quadratic(resp.,symplectic)LieYamaguti algebra.展开更多
This study mainly focuses on the triangle bounded L⁃algebras and triangle ideals.Firstly,the definition of triangle bounded L⁃algebras is presented,and several examples with different conditions are outlined along wit...This study mainly focuses on the triangle bounded L⁃algebras and triangle ideals.Firstly,the definition of triangle bounded L⁃algebras is presented,and several examples with different conditions are outlined along with an exploration of their properties.Moreover,we investigate the structure of triangle bounded L⁃algebra with a special condition.Secondly,we define the concept of triangle ideals of triangle bounded L⁃algebra and explore the connection between the triangle ideals of triangle bounded L⁃algebra L and the ideals of bounded L⁃algebra E(L).In addition,we classified and studied various classes of triangle ideals,including Stonean triangle ideals,extended Stonean triangle ideals,and lattice ideals,and by introducing the notion of Stonean triangle bounded L algebras,we examine the relationship between Stonean triangle bounded L⁃algebras and Stonean triangle ideals.Finally,we investigate the interrelationships among these various types of triangle ideals.展开更多
In this paper,we study anti-derivations and anti-left multipliers.For a class of algebras,which contains triangular algebras,matrix algebras,embedded algebras,Cuntz algebras,nest algebras,P-lattice algebras,and linear...In this paper,we study anti-derivations and anti-left multipliers.For a class of algebras,which contains triangular algebras,matrix algebras,embedded algebras,Cuntz algebras,nest algebras,P-lattice algebras,and linear transformation algebras L(X),we show that every anti-left multiplier on these algebras is zero.Furthermore,let A be a zero product determined algebra andδbe a linear mapping from A into itself,satisfying that for any a,b in A,ab=0 impliesδ(b)a+bδ(a)=0.We show thatδ(x)=D(x)+δ(1)x,where D is an anti-derivation andδ(1)∈Z(A).展开更多
In this paper,we shall study structures of even lattice vertex operator algebras by using the geometry of the varieties of their semi-conformal vectors.We first give the varieties of semi-conformal vectors of a family...In this paper,we shall study structures of even lattice vertex operator algebras by using the geometry of the varieties of their semi-conformal vectors.We first give the varieties of semi-conformal vectors of a family of vertex operator algebras V_(√kA_(1)) associated to rank-one positive definite even lattices √kA_(1) for arbitrary positive integers k to characterize these even lattice vertex operator algebras.In such a family of lattice vertex operator algebras V_(√kA_(1)),the vertex operator algebra V_(√2A_(1)) is different from others.Hence we describe the varieties of semi-conformal vectors of V_(√2A_(1)) and the fixed vertex operator subalgebra V^(+)√2A_(1).Moreover,as applications,we study the relations between vertex operator algebras V_(√kA_(1) )and L_(sl_(2))(k,0)for arbitrary positive integers k by the viewpoint of semi-conformal homomorphisms of vertex operator algebras.For case k=2,in the series of rational simple affine vertex operator algebras L_(sl_(2))(k,0)for positive integers k,we show that L_(sl_(2))(2,0)is a unique frame vertex operator algebra with rank 3.展开更多
In this paper,we first introduce the notion of relative Rota-Baxter operators of nonzero weight on 3-Hom-Lie algebras and define a cohomology of relative Rota-Baxter operators of nonzero weight on 3-Hom-Lie algebras w...In this paper,we first introduce the notion of relative Rota-Baxter operators of nonzero weight on 3-Hom-Lie algebras and define a cohomology of relative Rota-Baxter operators of nonzero weight on 3-Hom-Lie algebras with coefficients in a suitable representation.Next,we introduce and study 3-Hom-post-Lie-algebras as the underlying structure of relative Rota-Baxter operators of nonzero weight on 3-Hom-Lie algebras.Finally,we investigate relative Rota-Baxter operators of nonzero weight on 3-Hom-Lie algebras induced by Hom-Lie algebras.展开更多
In this paper,we introduce non-abelian cohomology groups and classify the nonabelian extensions of Rota-Baxter pre-Lie algebras in terms of non-abelian cohomology groups.Next,we explore the inducibility of pairs of au...In this paper,we introduce non-abelian cohomology groups and classify the nonabelian extensions of Rota-Baxter pre-Lie algebras in terms of non-abelian cohomology groups.Next,we explore the inducibility of pairs of automorphisms and derive the analog Wells exact sequences under the circumstance of Rota-Baxter pre-Lie algebras.Finally,we discuss the inducibility problem of pairs of automorphisms about an abelian extensions of Rota-Baxter pre-Lie algebras.展开更多
Let R be a commutative ring with unity and T be a triangular algebra over R.Let a sequence G={G_n}_(n∈N)of nonlinear mappings G_n:T→T associated with nonlinear Lie triple higher derivations∆={δ_n}_(n∈N)by local ac...Let R be a commutative ring with unity and T be a triangular algebra over R.Let a sequence G={G_n}_(n∈N)of nonlinear mappings G_n:T→T associated with nonlinear Lie triple higher derivations∆={δ_n}_(n∈N)by local actions be a generalized Lie triple higher derivation by local actions satisfying Gn([[x,y],z])=Σ_(i+j+k=n)[[Gi(x),δj(y)],δk(z)]for all x,y,z∈T with xyz=0.Under some mild conditions on T,we prove in this paper that every nonlinear generalized Lie triple higher derivation by local actions on triangular algebras is proper.As an application we shall give a characterization of nonlinear generalized Lie triple higher derivations by local actions on upper triangular matrix algebras and nest algebras,respectively.At the same time,it also improves some interesting conclusions,such as[J.Algebra Appl.22(3),2023,Paper No.2350059],[Axioms,11,2022,1–16].展开更多
Let A be a unital^(*)-algebra containing a nontrivial projection,N be the set of non-negative integers.Under some mild condi-tions on A,it is shown that any nonlinear mixed Jordan triple^(*)-higher derivation D={dn}n...Let A be a unital^(*)-algebra containing a nontrivial projection,N be the set of non-negative integers.Under some mild condi-tions on A,it is shown that any nonlinear mixed Jordan triple^(*)-higher derivation D={dn}n∈N is an additive^(*)-higher derivation.In particu-lar,we apply the above result to prime^(*)-algebras and von Neumann algebras with no central summands of typeⅠ1.展开更多
Let N be a nest of projections on a Hilbert space H and T(N) be the corresponding nest algebra. Let A be a large subalgebra of T(N). It is proved that any maximal n-nilpotent ideal of A is in the form of A∩R F,where...Let N be a nest of projections on a Hilbert space H and T(N) be the corresponding nest algebra. Let A be a large subalgebra of T(N). It is proved that any maximal n-nilpotent ideal of A is in the form of A∩R F,where F is a finite subnest of N and R F is the Jacobson radical of T(F).Using this result can prove that two large subalgebras are isomorphic if and only if the corresponding nests are similar.展开更多
Let P be a parabolic subalgebra of a general linear Lie algebra gl（n,F） over a field F, where n ≥ 3, F contains at least n different elements, and char（F） ≠ 2. In this article, we prove that generalized derivati...Let P be a parabolic subalgebra of a general linear Lie algebra gl（n,F） over a field F, where n ≥ 3, F contains at least n different elements, and char（F） ≠ 2. In this article, we prove that generalized derivations, quasiderivations, and product zero derivations of P coincide, and any generalized derivation of P is a sum of an inner derivation, a central quasiderivation, and a scalar multiplication map of P. We also show that any commuting automorphism of P is a central automorphism, and any commuting derivation of P is a central derivation.展开更多
In this article, we use the general method of quantization by Drinfeld’s twist to quantize explicitly the Lie bialgebra structures on Lie algebras of Block type.
In this article, Lie super-bialgebra structures on generalized super-Virasoro algebras/： are considered. It is proved that all such Lie super-bialgebras are coboundary triangular Lie super-bialgebras if and only if H...In this article, Lie super-bialgebra structures on generalized super-Virasoro algebras/： are considered. It is proved that all such Lie super-bialgebras are coboundary triangular Lie super-bialgebras if and only if Hi（ ） = 0.展开更多
Let T,U be two Artin algebras and_(U)M_(T)be a U-T-bimodule.In this paper,we get a necessary and sufficient condition such that the formal triangular matrix algebra Λ=(T 0 M U)is(m,n)-Igusa-Todorov when_(U)M,M_(T)are...Let T,U be two Artin algebras and_(U)M_(T)be a U-T-bimodule.In this paper,we get a necessary and sufficient condition such that the formal triangular matrix algebra Λ=(T 0 M U)is(m,n)-Igusa-Todorov when_(U)M,M_(T)are projective.We also study the Igusa-Todorov dimension of Λ.More specifically,it is proved that max{IT.dim T,IT.dim U}≤IT.dim Λ≤min{max{gl.dim T,IT.dim U},max{gl.dim U,IT.dim T}}.展开更多
The linear operations of the equivalent classes of crossed modules of Lie color algebras are studied. The set of the equivalent classes of crossed modules is proved to be a vector space, which is isomorphic with the h...The linear operations of the equivalent classes of crossed modules of Lie color algebras are studied. The set of the equivalent classes of crossed modules is proved to be a vector space, which is isomorphic with the homogeneous components of degree zero of the third cohomology group of Lie color algebras. As an application of this theory, the crossed modules of Witt type Lie color algebras is described, and the result is proved that there is only one equivalent class of the crossed modules of Witt type Lie color algebras when the abelian group Г is equal to Г＋. Finally, for a Witt type Lie color algebra, the classification of its crossed modules is obtained by the isomorphism between the third cohomology group and the crossed modules.展开更多
基金Supported by the National Natural Science Foundation of China(Grant Nos.11761017,11801150)the Science and Technology Foundation of Guizhou Province(Grant No.20201Y005)。
文摘In this paper,we give an explicit and systematic study on the double constructions of Frobenius Hom-algebras and introduce the close relations between O-operators and Homdendriform algebras.Furthermore,we study the double constructions of Connes cocycles in terms of Hom-dendriform algebras.Finally,we give a clear analogy between antisymmetric infinitesimal Hom-bialgebras and Hom-dendriform D-bialgebras.
基金Supported by National Natural Science Foundation of China(12271085)Supported by National Natural Science Foundation of Heilongjiang Province(LH2022A019)+3 种基金Basic Scientic Research Operating Funds for Provincial Universities in Heilongjiang Province(2020 KYYWF 1018)Heilongjiang University Outstanding Youth Science Foundation(JCL202103)Heilongjiang University Educational and Teaching Reform Research Project(2024C43)Heilongjiang University Postgraduate Education Reform Project(JGXM_YJS_2024010).
文摘In this paper,we study the Hom-structures of a special class of solvable Lie algebras with naturally graded filiform nilradical n_(n,1).Over an algebraically closed field F of zero characteristic,we calculate the Hom-structures of these solvable Lie algebras using the Hom-Jacobi identity,obtain the bases of these Hom-structures and observe that there are certain similarities among these bases.
基金Supported by the Universities Key Laboratory of System Modeling and Data Mining in Guizhou Province(Grant No.2023013)the National Natural Science Foundation of China(Grant No.12161013)the Science and Technology Program of Guizhou Province(Grant No.ZK[2023]025)。
文摘Semenov-Tian-Shansky has given the solution of the modified classical Yang-Baxter equation, which was called the modified r-matrix. Relevant studies have been extensive in recent times. In this paper, we introduce the concept and representations of modified RotaBaxter Hom-Lie algebras. We develop a cohomology of modified Rota-Baxter Hom-Lie algebras with coefficients in a suitable representation. As applications, we study formal deformations and abelian extensions of modified Rota-Baxter Hom-Lie algebras in terms of second cohomology groups.
基金Supported by the Fundamental Research Funds for the Central Universities
文摘Let F be a field of characteristic not 2, and let A be a finite-dimensional semisimple F -algebra. All local automorphisms of A are characterized when all the degrees of A are larger than 1. If F is further assumed to be an algebraically closed field of characteristic zero, K a finite group, F K the group algebra of K over F , then all local automorphisms of F K are also characterized.
基金Supported by NSFC(No.12101316)Belt and Road Innovative Talents Exchange Foreign Experts project(No.DL2023014002L)。
文摘In this paper,we show that an ideal generated by matching Rota-Baxter equations is a bideal of a Hopf algebra on decorated rooted forests.We then get a bialgebraic structure on the space of decorated rooted forests modulo this biideal.As an application,a connected graded bialgebra and so a graded Hopf algebra on matching Rota-Baxter algebras are constructed,which simplifies the Hopf algebraic structure proposed by[Pacific J.Math.,2022,317(2):441-475].
基金National Natural Science Foundation of China(12161013)Research Projects of Guizhou University of Commerce in 2024。
文摘The modifiedλ-differential Lie-Yamaguti algebras are considered,in which a modifiedλ-differential Lie-Yamaguti algebra consisting of a Lie-Yamaguti algebra and a modifiedλ-differential operator.First we introduce the representation of modifiedλ-differential Lie-Yamaguti algebras.Furthermore,we establish the cohomology of a modifiedλ-differential Lie-Yamaguti algebra with coefficients in a representation.Finally,we investigate the one-parameter formal deformations and Abelian extensions of modifiedλ-differential Lie-Yamaguti algebras using the second cohomology group.
文摘A left Leibniz algebra equipped with an invariant nondegenerate skew-symmetric bilinear form(i.e.,a skew-symmetric quadratic Leibniz algebra)is constructed.The notion of T^(*)-extension of Lie-Yamaguti algebras is introduced and it is observed that the trivial extension of a Lie-Yamaguti algebra is a quadratic Lie-Yamaguti algebra.It is proved that every symmetric(resp.,skew-symmetric)quadratic Leibniz algebra induces a quadratic(resp.,symplectic)LieYamaguti algebra.
基金Sponsored by Foreign Expert Program of China(Grant No.DL2023041002L)Yulin City Industry University Research Project(Grant No.CXY-2022-59).
文摘This study mainly focuses on the triangle bounded L⁃algebras and triangle ideals.Firstly,the definition of triangle bounded L⁃algebras is presented,and several examples with different conditions are outlined along with an exploration of their properties.Moreover,we investigate the structure of triangle bounded L⁃algebra with a special condition.Secondly,we define the concept of triangle ideals of triangle bounded L⁃algebra and explore the connection between the triangle ideals of triangle bounded L⁃algebra L and the ideals of bounded L⁃algebra E(L).In addition,we classified and studied various classes of triangle ideals,including Stonean triangle ideals,extended Stonean triangle ideals,and lattice ideals,and by introducing the notion of Stonean triangle bounded L algebras,we examine the relationship between Stonean triangle bounded L⁃algebras and Stonean triangle ideals.Finally,we investigate the interrelationships among these various types of triangle ideals.
基金Supported by the General Program of Shanghai Natural Science Foundation(Grant No.24ZR1415600)the National Natural Science Foundation of China(Grant Nos.1232637412401157)。
文摘In this paper,we study anti-derivations and anti-left multipliers.For a class of algebras,which contains triangular algebras,matrix algebras,embedded algebras,Cuntz algebras,nest algebras,P-lattice algebras,and linear transformation algebras L(X),we show that every anti-left multiplier on these algebras is zero.Furthermore,let A be a zero product determined algebra andδbe a linear mapping from A into itself,satisfying that for any a,b in A,ab=0 impliesδ(b)a+bδ(a)=0.We show thatδ(x)=D(x)+δ(1)x,where D is an anti-derivation andδ(1)∈Z(A).
基金Supported by National Natural Science Foundation of China(Grant No.12475002).
文摘In this paper,we shall study structures of even lattice vertex operator algebras by using the geometry of the varieties of their semi-conformal vectors.We first give the varieties of semi-conformal vectors of a family of vertex operator algebras V_(√kA_(1)) associated to rank-one positive definite even lattices √kA_(1) for arbitrary positive integers k to characterize these even lattice vertex operator algebras.In such a family of lattice vertex operator algebras V_(√kA_(1)),the vertex operator algebra V_(√2A_(1)) is different from others.Hence we describe the varieties of semi-conformal vectors of V_(√2A_(1)) and the fixed vertex operator subalgebra V^(+)√2A_(1).Moreover,as applications,we study the relations between vertex operator algebras V_(√kA_(1) )and L_(sl_(2))(k,0)for arbitrary positive integers k by the viewpoint of semi-conformal homomorphisms of vertex operator algebras.For case k=2,in the series of rational simple affine vertex operator algebras L_(sl_(2))(k,0)for positive integers k,we show that L_(sl_(2))(2,0)is a unique frame vertex operator algebra with rank 3.
基金Supported by the National Natural Science Foundation of China(Grant No.12161013)the School-Level Student Research Project of Guizhou University of Finance and Economics(Grant No.2024ZXSY231)。
文摘In this paper,we first introduce the notion of relative Rota-Baxter operators of nonzero weight on 3-Hom-Lie algebras and define a cohomology of relative Rota-Baxter operators of nonzero weight on 3-Hom-Lie algebras with coefficients in a suitable representation.Next,we introduce and study 3-Hom-post-Lie-algebras as the underlying structure of relative Rota-Baxter operators of nonzero weight on 3-Hom-Lie algebras.Finally,we investigate relative Rota-Baxter operators of nonzero weight on 3-Hom-Lie algebras induced by Hom-Lie algebras.
基金Supported by the National Natural Science Foundation of China(Grant No.12161013)the School-Level Student Research Project of Guizhou University of Finance and Economics(Grant No.2024ZXSY239).
文摘In this paper,we introduce non-abelian cohomology groups and classify the nonabelian extensions of Rota-Baxter pre-Lie algebras in terms of non-abelian cohomology groups.Next,we explore the inducibility of pairs of automorphisms and derive the analog Wells exact sequences under the circumstance of Rota-Baxter pre-Lie algebras.Finally,we discuss the inducibility problem of pairs of automorphisms about an abelian extensions of Rota-Baxter pre-Lie algebras.
基金Supported by Open Research Fund of Hubei Key Laboratory of Mathematical Sciences(Central China Normal University)the Natural Science Foundation of Anhui Province(Grant No.2008085QA01)the University Natural Science Research Project of Anhui Province(Grant No.KJ2019A0107)。
文摘Let R be a commutative ring with unity and T be a triangular algebra over R.Let a sequence G={G_n}_(n∈N)of nonlinear mappings G_n:T→T associated with nonlinear Lie triple higher derivations∆={δ_n}_(n∈N)by local actions be a generalized Lie triple higher derivation by local actions satisfying Gn([[x,y],z])=Σ_(i+j+k=n)[[Gi(x),δj(y)],δk(z)]for all x,y,z∈T with xyz=0.Under some mild conditions on T,we prove in this paper that every nonlinear generalized Lie triple higher derivation by local actions on triangular algebras is proper.As an application we shall give a characterization of nonlinear generalized Lie triple higher derivations by local actions on upper triangular matrix algebras and nest algebras,respectively.At the same time,it also improves some interesting conclusions,such as[J.Algebra Appl.22(3),2023,Paper No.2350059],[Axioms,11,2022,1–16].
基金Supported by the National Natural Science Foundation of China(12271323)。
文摘Let A be a unital^(*)-algebra containing a nontrivial projection,N be the set of non-negative integers.Under some mild condi-tions on A,it is shown that any nonlinear mixed Jordan triple^(*)-higher derivation D={dn}n∈N is an additive^(*)-higher derivation.In particu-lar,we apply the above result to prime^(*)-algebras and von Neumann algebras with no central summands of typeⅠ1.
文摘Let N be a nest of projections on a Hilbert space H and T(N) be the corresponding nest algebra. Let A be a large subalgebra of T(N). It is proved that any maximal n-nilpotent ideal of A is in the form of A∩R F,where F is a finite subnest of N and R F is the Jacobson radical of T(F).Using this result can prove that two large subalgebras are isomorphic if and only if the corresponding nests are similar.
基金supported by the National Natural Science Foundation of China(11101084,11071040)the Fujian Province Nature Science Foundation of China(2013J01005)
文摘Let P be a parabolic subalgebra of a general linear Lie algebra gl（n,F） over a field F, where n ≥ 3, F contains at least n different elements, and char（F） ≠ 2. In this article, we prove that generalized derivations, quasiderivations, and product zero derivations of P coincide, and any generalized derivation of P is a sum of an inner derivation, a central quasiderivation, and a scalar multiplication map of P. We also show that any commuting automorphism of P is a central automorphism, and any commuting derivation of P is a central derivation.
基金supported by the National Science Foundation of China (10825101)"One Hundred Talents Program" from University of Science and Technology of Chinathe China Postdoctoral Science Foundation (20090450810)
文摘In this article, we use the general method of quantization by Drinfeld’s twist to quantize explicitly the Lie bialgebra structures on Lie algebras of Block type.
基金Supported by the Foundation of Shanghai Education Committee (06FZ029)NSF of China (10471091)"One Hundred Program" from University of Science and Technology of China
文摘In this article, Lie super-bialgebra structures on generalized super-Virasoro algebras/： are considered. It is proved that all such Lie super-bialgebras are coboundary triangular Lie super-bialgebras if and only if Hi（ ） = 0.
基金Supported by the National Natural Science Foundation of China(Grant No.12301041)the Science Foundation for Distinguished Young Scholars of Anhui Province(Grant No.2108085J01)。
文摘Let T,U be two Artin algebras and_(U)M_(T)be a U-T-bimodule.In this paper,we get a necessary and sufficient condition such that the formal triangular matrix algebra Λ=(T 0 M U)is(m,n)-Igusa-Todorov when_(U)M,M_(T)are projective.We also study the Igusa-Todorov dimension of Λ.More specifically,it is proved that max{IT.dim T,IT.dim U}≤IT.dim Λ≤min{max{gl.dim T,IT.dim U},max{gl.dim U,IT.dim T}}.
基金The Natural Science Foundation of Jiangsu Province(No.BK2012736)the Natural Science Foundation of Chuzhou University(No.2010kj006Z)
文摘The linear operations of the equivalent classes of crossed modules of Lie color algebras are studied. The set of the equivalent classes of crossed modules is proved to be a vector space, which is isomorphic with the homogeneous components of degree zero of the third cohomology group of Lie color algebras. As an application of this theory, the crossed modules of Witt type Lie color algebras is described, and the result is proved that there is only one equivalent class of the crossed modules of Witt type Lie color algebras when the abelian group Г is equal to Г＋. Finally, for a Witt type Lie color algebra, the classification of its crossed modules is obtained by the isomorphism between the third cohomology group and the crossed modules.
