This paper focuses on the finite dimensional irreducible representations of Lie superalgebra D(2,1;α).We explicitly construct the finite dimensional representations of the superalgebra D(2,1;α)by using the shift ope...This paper focuses on the finite dimensional irreducible representations of Lie superalgebra D(2,1;α).We explicitly construct the finite dimensional representations of the superalgebra D(2,1;α)by using the shift operator and differential operator representations.Unlike ordinary Lie algebra representation,there are typical and atypical representations for most superalgebras.Therefore,its typical and atypical representation conditions are also given.Our results are expected to be useful for the construction of primary fields of the corresponding current superalgebra of D(2,1;α).展开更多
The aim of this article is to introduce the notion of Hom-Lie H-pseudo-superalgebras for any Hopf algebra H. This class of algebras is a natural generalization of the Hom-Lie pseudo-algebras as well as a special case ...The aim of this article is to introduce the notion of Hom-Lie H-pseudo-superalgebras for any Hopf algebra H. This class of algebras is a natural generalization of the Hom-Lie pseudo-algebras as well as a special case of the Hom-Lie superalgebras. We present some construction theorems of Hom-Lie H-pseudo-superalgebras, reformulate the equivalent definition of Hom-Lie H-pseudo-super-algebras, and consider the cohomology theory of Hom-Lie H-pseudo-superalgebras with coefficients in arbitrary Hom-modules as a generalization of Kac’s result.展开更多
In the present article, the authors give some properties on subinvariant subalgebras of modular Lie superalgebras and obtain the derivation tower theorem of modular Lie superalgebras, which is analogous to the automor...In the present article, the authors give some properties on subinvariant subalgebras of modular Lie superalgebras and obtain the derivation tower theorem of modular Lie superalgebras, which is analogous to the automorphism tower theorem of finite groups. Moreover, they announce and prove some results of modular complete Lie superalgebras.展开更多
This paper presents a sufficient condition for the cohomology groups of an associative superalgebra to vanish. As its application, we prove that the cohomology groups H n(L,M) vanish when L is a strongly semi...This paper presents a sufficient condition for the cohomology groups of an associative superalgebra to vanish. As its application, we prove that the cohomology groups H n(L,M) vanish when L is a strongly semisimple Lie superalgebra and M is an irreducible faithful L module.展开更多
Homogeneous and inhornogeneous differential realizations of the OSP(2,1)superalgebra on the spaces of homogeneous and inhomogeneous polynomials and the corresponding boson-fermioii realizations are studied.The new ind...Homogeneous and inhornogeneous differential realizations of the OSP(2,1)superalgebra on the spaces of homogeneous and inhomogeneous polynomials and the corresponding boson-fermioii realizations are studied.The new indecomposable and irreducible representations of the OSP(2,1)are given on subspaces and quotient spaces of the universal enveloping algebras of Heisenberg-Weyl superalgebra.All the finite dimensional irreducible representation of the OSP(2,1)superalgebra is naturally obtained as special cases.展开更多
In this paper we mainly study the negative Z-homogeneous derivations from the even part of the finite-dimensional odd Hamiltonian superalgebra HO into the odd part of generalized Witt superalgebra W over a field of pr...In this paper we mainly study the negative Z-homogeneous derivations from the even part of the finite-dimensional odd Hamiltonian superalgebra HO into the odd part of generalized Witt superalgebra W over a field of prime characteristic p 〉 3. Using the gener- ating set of 7-EO, by means of calculating actions of derivations on the generating set, we first compute the derivations of Z-degree -1, then determine the derivations of Z-degree less than --1.展开更多
In this paper, some properties of perfect Lie superalgebras are investigated. We prove that the derivation superalgebra of a centerless perfect Lie superalgebra of arbitrary dimension over a field of arbitrary charact...In this paper, some properties of perfect Lie superalgebras are investigated. We prove that the derivation superalgebra of a centerless perfect Lie superalgebra of arbitrary dimension over a field of arbitrary characteristic is complete and we obtain a necessary and sufficient condition for the holomorph of a centerless perfect Lie superalgebra to be complete. Finally, some properties of perfect restricted Lie superalgebras are given.展开更多
Compactness of subspaces of a Z<sub>2</sub>-graded vector space is introduced and used to study simple Leibniz superalgebras. We introduce left and right super-invariance of bilinear forms over superalgebr...Compactness of subspaces of a Z<sub>2</sub>-graded vector space is introduced and used to study simple Leibniz superalgebras. We introduce left and right super-invariance of bilinear forms over superalgebras. Pseudo-quadratic Leibniz superalgebras are Leibniz superalgebras endowed with a non degenerate, supersymmetric and super-invariant bilinear form. In this paper, we show that every nondegenerate, supersymmetric and super-invariant bilinear form over a Leibniz superalgebra induce a Lie superalgebra over the underlying vector space. Then by using double extension extended to Leibniz superalgebras, we study pseudo-quadratic Leibniz superalgebras and the induced Lie superalgebras. In particular, we generalize some results on Leibniz algebras to Leibniz superalgebras.展开更多
Let F be a field and char F = p > 3. In this paper the derivation algebras of Lie superalgebras W and S of Cartan-type over F are determined by the calculating method.
The filtration structure of finite-dimensional special odd Hamilton superalgebras over a field of prime characteristic was studied. By determining ad-nilpotent dements in the even part, the natural filtration of speci...The filtration structure of finite-dimensional special odd Hamilton superalgebras over a field of prime characteristic was studied. By determining ad-nilpotent dements in the even part, the natural filtration of special odd Hamiltonian superalgebras is proved to be invariant. Using this result, the special odd Hamilton superalgebras is classified. Finally, the automorphism group of the restricted special odd Hamilton superalgebras is determined.展开更多
Let gl0|2 be a subalgebra of the general linear Lie superalgebra.In this paper,outer derivations from gl0|2 to the generalized Witt Lie superalgebra are completely determined by matrices.
In this paper we first prove the PBW theorem for reduced universal enveloping algebras of restricted Lie superalgebras. Then the notion of an induced module is introduced and the dimension formula of induced modules i...In this paper we first prove the PBW theorem for reduced universal enveloping algebras of restricted Lie superalgebras. Then the notion of an induced module is introduced and the dimension formula of induced modules is established. Finally, using the results above, we obtain a property of induced modules pertaining to automorphisms of Lie superalgebras and isomorphisms of modules.展开更多
Let F be an algebraically closed field of characteristic zero, and L be a basic classical Lie superalgebra except A（n, n） over F. In this paper, we prove that every 2-local superderivation on L is a superderivation....Let F be an algebraically closed field of characteristic zero, and L be a basic classical Lie superalgebra except A（n, n） over F. In this paper, we prove that every 2-local superderivation on L is a superderivation. Furthermore, we give an example to show that a subalgebra of spl（2, 2） admits a 2-local superderivation which is not a superderivation.展开更多
In this paper, we determine all maximal graded subalgebras of the general linear Lie superalgebras containing the standard Cartan subalgebras over a unital supercommutative superring with 2 invertible.
We propose the supereonneetion formalism to construct the off-shell BRST-VSUSY superalgebra for D = 4 BF theories. The method is based on the natural introduction of physical fields as well as auxiliary fields via sup...We propose the supereonneetion formalism to construct the off-shell BRST-VSUSY superalgebra for D = 4 BF theories. The method is based on the natural introduction of physical fields as well as auxiliary fields via supereon- neetions and their associated supereurvatures defined on a superspaee. We also give a prescription to build the off-shell BRST-VSUSY exact quantum action.展开更多
We prove that each finitely generated (as a module) complete color Lie superalgebras over noetherian ring can be decomposed uniquely into a direct sum of complete simple ideals.
A new eight-dimensional Lie superalgebra is constructed and two isospectral problems with six potentials are designed. Corresponding hierarchies of nonlinear evolution equations, as well as super-AKNS and super-Levi, ...A new eight-dimensional Lie superalgebra is constructed and two isospectral problems with six potentials are designed. Corresponding hierarchies of nonlinear evolution equations, as well as super-AKNS and super-Levi, are derived. Their super-Hamiltonian structures are established by making use of the supertrace identity, and they are integrable in the sense of Liouville.展开更多
In this paper, the definitions and some properties of n-Lie superalgebras are presented. Our main aim is to study the decomposition and uniqueness of finite dimensional n-Lie superalgebras with trivial center. Aecodin...In this paper, the definitions and some properties of n-Lie superalgebras are presented. Our main aim is to study the decomposition and uniqueness of finite dimensional n-Lie superalgebras with trivial center. Aecoding to the decomposition of n-Lie superalgebras, we obtain the decomposition of inner derivation superalgebras and derivation superalgebras respectively. Furthermore, we discuss some properties about the centroid of n-Lie superalgebras, so we can see its application in the decomposition of n-Lie superalgebras.展开更多
基金financial support from the National Natural Science Foundation of China(Grant No.11405051)supported by the Australian Research Council Discovery Project DP190101529supported by NSFC Grant 11775299。
文摘This paper focuses on the finite dimensional irreducible representations of Lie superalgebra D(2,1;α).We explicitly construct the finite dimensional representations of the superalgebra D(2,1;α)by using the shift operator and differential operator representations.Unlike ordinary Lie algebra representation,there are typical and atypical representations for most superalgebras.Therefore,its typical and atypical representation conditions are also given.Our results are expected to be useful for the construction of primary fields of the corresponding current superalgebra of D(2,1;α).
文摘The aim of this article is to introduce the notion of Hom-Lie H-pseudo-superalgebras for any Hopf algebra H. This class of algebras is a natural generalization of the Hom-Lie pseudo-algebras as well as a special case of the Hom-Lie superalgebras. We present some construction theorems of Hom-Lie H-pseudo-superalgebras, reformulate the equivalent definition of Hom-Lie H-pseudo-super-algebras, and consider the cohomology theory of Hom-Lie H-pseudo-superalgebras with coefficients in arbitrary Hom-modules as a generalization of Kac’s result.
基金Supported by Youth Science Foundation of Northeast Normal University (111494027) National Natural Science Foundation of China (10271076)
文摘In the present article, the authors give some properties on subinvariant subalgebras of modular Lie superalgebras and obtain the derivation tower theorem of modular Lie superalgebras, which is analogous to the automorphism tower theorem of finite groups. Moreover, they announce and prove some results of modular complete Lie superalgebras.
文摘This paper presents a sufficient condition for the cohomology groups of an associative superalgebra to vanish. As its application, we prove that the cohomology groups H n(L,M) vanish when L is a strongly semisimple Lie superalgebra and M is an irreducible faithful L module.
文摘Homogeneous and inhornogeneous differential realizations of the OSP(2,1)superalgebra on the spaces of homogeneous and inhomogeneous polynomials and the corresponding boson-fermioii realizations are studied.The new indecomposable and irreducible representations of the OSP(2,1)are given on subspaces and quotient spaces of the universal enveloping algebras of Heisenberg-Weyl superalgebra.All the finite dimensional irreducible representation of the OSP(2,1)superalgebra is naturally obtained as special cases.
基金Supported by the Scientific Research Fund of Heilongjiang Provincial Education Department(GrantNo.12521114)the Science Foundation for Young Scholars,Harbin University of Science and Technology(GrantNo.2011YF006)+1 种基金the National Natural Science Foundation of China(Grant No.11171055)the Natural Science Foundation for Distinguished Young Scholars of Heilongjiang Province(Grant No.JC201004)
文摘In this paper we mainly study the negative Z-homogeneous derivations from the even part of the finite-dimensional odd Hamiltonian superalgebra HO into the odd part of generalized Witt superalgebra W over a field of prime characteristic p 〉 3. Using the gener- ating set of 7-EO, by means of calculating actions of derivations on the generating set, we first compute the derivations of Z-degree -1, then determine the derivations of Z-degree less than --1.
文摘In this paper, some properties of perfect Lie superalgebras are investigated. We prove that the derivation superalgebra of a centerless perfect Lie superalgebra of arbitrary dimension over a field of arbitrary characteristic is complete and we obtain a necessary and sufficient condition for the holomorph of a centerless perfect Lie superalgebra to be complete. Finally, some properties of perfect restricted Lie superalgebras are given.
文摘Compactness of subspaces of a Z<sub>2</sub>-graded vector space is introduced and used to study simple Leibniz superalgebras. We introduce left and right super-invariance of bilinear forms over superalgebras. Pseudo-quadratic Leibniz superalgebras are Leibniz superalgebras endowed with a non degenerate, supersymmetric and super-invariant bilinear form. In this paper, we show that every nondegenerate, supersymmetric and super-invariant bilinear form over a Leibniz superalgebra induce a Lie superalgebra over the underlying vector space. Then by using double extension extended to Leibniz superalgebras, we study pseudo-quadratic Leibniz superalgebras and the induced Lie superalgebras. In particular, we generalize some results on Leibniz algebras to Leibniz superalgebras.
文摘Let F be a field and char F = p > 3. In this paper the derivation algebras of Lie superalgebras W and S of Cartan-type over F are determined by the calculating method.
基金Sponsored by the Scientific Research Fund of Heilongjiang Provincial Education Department (11541109)the Science Foundation of Harbin Normal University (KM2007-11)
文摘The filtration structure of finite-dimensional special odd Hamilton superalgebras over a field of prime characteristic was studied. By determining ad-nilpotent dements in the even part, the natural filtration of special odd Hamiltonian superalgebras is proved to be invariant. Using this result, the special odd Hamilton superalgebras is classified. Finally, the automorphism group of the restricted special odd Hamilton superalgebras is determined.
基金the Fundamental Research Fund(2572018BC15)for the Central Universitiesthe NSF(11171055)of China
文摘Let gl0|2 be a subalgebra of the general linear Lie superalgebra.In this paper,outer derivations from gl0|2 to the generalized Witt Lie superalgebra are completely determined by matrices.
文摘In this paper we first prove the PBW theorem for reduced universal enveloping algebras of restricted Lie superalgebras. Then the notion of an induced module is introduced and the dimension formula of induced modules is established. Finally, using the results above, we obtain a property of induced modules pertaining to automorphisms of Lie superalgebras and isomorphisms of modules.
基金Supported by the National Natural Science Foundation of China(Grant No.11471090)
文摘Let F be an algebraically closed field of characteristic zero, and L be a basic classical Lie superalgebra except A（n, n） over F. In this paper, we prove that every 2-local superderivation on L is a superderivation. Furthermore, we give an example to show that a subalgebra of spl（2, 2） admits a 2-local superderivation which is not a superderivation.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1117105511471090)the Natural Science Foundation of the Education Department of Heilongjiang Province(Grant No.12521158)
文摘In this paper, we determine all maximal graded subalgebras of the general linear Lie superalgebras containing the standard Cartan subalgebras over a unital supercommutative superring with 2 invertible.
基金Acknowledgment M. Tahiri would like to thank the Alexander von Humboldt Stiftung for support and Prof. W. Rfihl （Department of Physics, Kaiserslautern University of Technology） for hospitality.
文摘We propose the supereonneetion formalism to construct the off-shell BRST-VSUSY superalgebra for D = 4 BF theories. The method is based on the natural introduction of physical fields as well as auxiliary fields via supereon- neetions and their associated supereurvatures defined on a superspaee. We also give a prescription to build the off-shell BRST-VSUSY exact quantum action.
文摘We prove that each finitely generated (as a module) complete color Lie superalgebras over noetherian ring can be decomposed uniquely into a direct sum of complete simple ideals.
基金Project supported by the Science Foundation of the Educational Department of Shandong Province of China (Grant No.J07YH01)
文摘A new eight-dimensional Lie superalgebra is constructed and two isospectral problems with six potentials are designed. Corresponding hierarchies of nonlinear evolution equations, as well as super-AKNS and super-Levi, are derived. Their super-Hamiltonian structures are established by making use of the supertrace identity, and they are integrable in the sense of Liouville.
文摘In this paper, the definitions and some properties of n-Lie superalgebras are presented. Our main aim is to study the decomposition and uniqueness of finite dimensional n-Lie superalgebras with trivial center. Aecoding to the decomposition of n-Lie superalgebras, we obtain the decomposition of inner derivation superalgebras and derivation superalgebras respectively. Furthermore, we discuss some properties about the centroid of n-Lie superalgebras, so we can see its application in the decomposition of n-Lie superalgebras.
