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
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
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 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.
The natural filtrations of the infinite-dimensional modular Lie superalgebra SHO＇ are proved to be invariant under automorphisms of SHO＇. The proof involves the investigation of the ad-nilpotent elements of the even...The natural filtrations of the infinite-dimensional modular Lie superalgebra SHO＇ are proved to be invariant under automorphisms of SHO＇. The proof involves the investigation of the ad-nilpotent elements of the even part, and the determination of the subalgebras generated by certain ad-nilpotent elements. A property of automorphisms of these Lie superalgebras can be established, and an intrinsic characterization of SHO＇ can be obtained.展开更多
We gived the definition of Hom-Leibniz superalgebra and studied its basic properties. In particular, the derivations of Hom-Leibniz Superalgebras are portrayed in detail.
We review our recent results on computation of the higher genus characters for vertex operator superalgebras modules. The vertex operator formal parameters are associated to local parameters on Riemann surfaces formed...We review our recent results on computation of the higher genus characters for vertex operator superalgebras modules. The vertex operator formal parameters are associated to local parameters on Riemann surfaces formed in one of two schemes of (self- or tori- ) sewing of lower genus Riemann surfaces. For the free fermion vertex operator superalgebra we present a closed formula for the genus two continuous orbifold partition functions (in either sewings) in terms of an infinite dimensional determinant with entries arising from the original torus Szeg? kernel. This partition function is holomorphic in the sewing parameters on a given suitable domain and possesses natural modular properties. Several higher genus generalizations of classical (including Fay’s and Jacobi triple product) identities show up in a natural way in the vertex operator algebra approach.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.
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
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
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
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.
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
Let L be a finite dimensional simple Lie superalgebra, and a sufficient condition is obtained for the length of transitive filtration of L to be greater than zero.
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
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.
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the Science Foundation of Harbin Normal University(KM2007-11)
文摘The natural filtrations of the infinite-dimensional modular Lie superalgebra SHO＇ are proved to be invariant under automorphisms of SHO＇. The proof involves the investigation of the ad-nilpotent elements of the even part, and the determination of the subalgebras generated by certain ad-nilpotent elements. A property of automorphisms of these Lie superalgebras can be established, and an intrinsic characterization of SHO＇ can be obtained.
基金Supported by the National Natural Science Foundation of China（10871057, 11171055）
文摘We gived the definition of Hom-Leibniz superalgebra and studied its basic properties. In particular, the derivations of Hom-Leibniz Superalgebras are portrayed in detail.
文摘We review our recent results on computation of the higher genus characters for vertex operator superalgebras modules. The vertex operator formal parameters are associated to local parameters on Riemann surfaces formed in one of two schemes of (self- or tori- ) sewing of lower genus Riemann surfaces. For the free fermion vertex operator superalgebra we present a closed formula for the genus two continuous orbifold partition functions (in either sewings) in terms of an infinite dimensional determinant with entries arising from the original torus Szeg? kernel. This partition function is holomorphic in the sewing parameters on a given suitable domain and possesses natural modular properties. Several higher genus generalizations of classical (including Fay’s and Jacobi triple product) identities show up in a natural way in the vertex operator algebra approach.
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.
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.
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.
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.
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.
文摘Let L be a finite dimensional simple Lie superalgebra, and a sufficient condition is obtained for the length of transitive filtration of L to be greater than zero.
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.
基金the National Natural Science Foundation of China(Grant No.11171055)the Natural ScienceFoundation of Jilin Province(Grant No.20130101068)the Fundamental Research Funds for the CentralUniversities(Grant No.12SSXT139)
文摘This paper is concerned with two results for （α, β, γ）-superderivations of general superalgebras over the field of complex numbers.
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.
