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
In this article the ■-graded transitive modular Lie superalgebra ⊕_(i≥-1)L_i,whose repre- sentation of L_o in L_(-1)is isomorphic to the natural representation of osp(L_(-1)),is determined.
A new family of finite-dimensional simple modular Lie superalgebra M is constructed based on results of Y. Z. Zhang and Q. C. Zhang [J. Algebra, 2009, 321： 3601-3619]. The simplicity and generators of M are discussed...A new family of finite-dimensional simple modular Lie superalgebra M is constructed based on results of Y. Z. Zhang and Q. C. Zhang [J. Algebra, 2009, 321： 3601-3619]. The simplicity and generators of M are discussed and the derivation superalgebra of M is characterized. Furthermore, the invariance of the nonnatural filtration of M is determined by the method of minimal dimension of image spaces.展开更多
This gives some identities of associative Lie superalgebras and some properties of modular Lie superalgebras. Furthermore, the primary decomposition theorem of modular Lie superalgebras is shown. It is well known that...This gives some identities of associative Lie superalgebras and some properties of modular Lie superalgebras. Furthermore, the primary decomposition theorem of modular Lie superalgebras is shown. It is well known that the primary decomposition theorem of modular Lie algebras has played an important role in the classification of the finite-dimensional simple modular Lie algebras （see [5, 6]）. Analogously, the primary decomposition theorem of modular Lie superalgebras may play an important role in the open classification of the finite dimensional simple modular Lie superalgebras.展开更多
Y. Z. Zhang and Q. C. Zhang [J. Algebra, 2009, 321： 3601-3619] constructed a new family of finite-dimensional modular Lie superalgebra Ω. Let Ω denote the even part of the Lie superalgebra Ω. We first give the gen...Y. Z. Zhang and Q. C. Zhang [J. Algebra, 2009, 321： 3601-3619] constructed a new family of finite-dimensional modular Lie superalgebra Ω. Let Ω denote the even part of the Lie superalgebra Ω. We first give the generator sets of the Lie algebra Ω. Then, we reduce the derivation of Ω to a certain form. With the reduced derivation and a torus of Ω, we determine the derivation algebra of Ω.展开更多
The authors consider a family of finite-dimensional Lie superalgebras of C-type over an algebraically closed field of characteristic p 〉 3. It is proved that the Lie superalgebras of C-type are simple and the spannin...The authors consider a family of finite-dimensional Lie superalgebras of C-type over an algebraically closed field of characteristic p 〉 3. It is proved that the Lie superalgebras of C-type are simple and the spanning sets are determined. Then the spanning sets are employed to characterize the superderivation algebras of these Lie superalgebras. Finally, the associative forms are discussed and a comparison is made between these Lie superalgebras and other simple Lie superalgebras of Cartan type.展开更多
In this paper F always denotes a field of characteristic p 〉 2. We construct the finitedimensional modular Lie superalgebra W（m,n, l, t_） over a field F, define θ-type derivation and determine the derivation super...In this paper F always denotes a field of characteristic p 〉 2. We construct the finitedimensional modular Lie superalgebra W（m,n, l, t_） over a field F, define θ-type derivation and determine the derivation superalgebra of W（m, n, l, t_）.展开更多
Let F be the underlying base field of characteristic p 〉 3 and denote by M the even part of the finite-dimensional simple modular Lie superalgebra M. In this paper, the generator sets of the Lie algebra M which will ...Let F be the underlying base field of characteristic p 〉 3 and denote by M the even part of the finite-dimensional simple modular Lie superalgebra M. In this paper, the generator sets of the Lie algebra M which will be heavily used to consider the derivation algebra Der（M） are given. Furthermore, the derivation algebra of M is determined by reducing derivations and a torus of M, i.e., Der（m）=ad（m） spanF{∏l ad （ξr＋1ξl）} spanF{adxi,ad（xiξ^v）∏ad（ξr＋1ξl）}. As a result, the derivation algebra of the even part of M does not equal the even part of the derivation superalgebra of M.展开更多
Let F be the underlying base field of characteristic p>3 and denote by Гo the even part of the finite-dimensional Lie superalgebra T.We give the generator sets of the Lie algebra Гo.Using certain properties of th...Let F be the underlying base field of characteristic p>3 and denote by Гo the even part of the finite-dimensional Lie superalgebra T.We give the generator sets of the Lie algebra Гo.Using certain properties of the canonical tori of Гo,we describe explicitly the derivation algebra of Гo.展开更多
The embedding theorem is established for Z-graded transitive modular Lie superalgebras g■■■(g-1)satisfying the conditions: (i)g0■■(g-1) and g0-module g-1 is isomorphic to the natural■(g-1)-module; (ii)dim g1=2/3...The embedding theorem is established for Z-graded transitive modular Lie superalgebras g■■■(g-1)satisfying the conditions: (i)g0■■(g-1) and g0-module g-1 is isomorphic to the natural■(g-1)-module; (ii)dim g1=2/3n(2n^2+1),where n=1/2dim g-1. In particular,it is proved that the finite-dimensional simple modular Lie superalgebras satisfying the conditions above are isomorphic to the odd Hamiltonian superalgebras.The restricted Lie superalgebras are also considered.展开更多
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
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.
基金Project supported by the NNSF (10271076)EMNSF (99036) of China
文摘In this article the ■-graded transitive modular Lie superalgebra ⊕_(i≥-1)L_i,whose repre- sentation of L_o in L_(-1)is isomorphic to the natural representation of osp(L_(-1)),is determined.
基金Acknowledgements The authors are grateful to the referees for their valuable comments and suggestions. This work was supported by the National Natural Science Foundation of China （Grant No. 11171055）, the Natural Science Foundation of Jilin Province （No. 201115006） Scientific Research Foundation for Returned Scholars Ministry of Education of China, and the Fundamental Research Funds for the Central Universities.
文摘A new family of finite-dimensional simple modular Lie superalgebra M is constructed based on results of Y. Z. Zhang and Q. C. Zhang [J. Algebra, 2009, 321： 3601-3619]. The simplicity and generators of M are discussed and the derivation superalgebra of M is characterized. Furthermore, the invariance of the nonnatural filtration of M is determined by the method of minimal dimension of image spaces.
基金Project supported by the National Natural Science Foundation of China (No.10271076) the Youth Science Foundation of Northeast Normal University (No. 111494027).
文摘This gives some identities of associative Lie superalgebras and some properties of modular Lie superalgebras. Furthermore, the primary decomposition theorem of modular Lie superalgebras is shown. It is well known that the primary decomposition theorem of modular Lie algebras has played an important role in the classification of the finite-dimensional simple modular Lie algebras （see [5, 6]）. Analogously, the primary decomposition theorem of modular Lie superalgebras may play an important role in the open classification of the finite dimensional simple modular Lie superalgebras.
文摘Y. Z. Zhang and Q. C. Zhang [J. Algebra, 2009, 321： 3601-3619] constructed a new family of finite-dimensional modular Lie superalgebra Ω. Let Ω denote the even part of the Lie superalgebra Ω. We first give the generator sets of the Lie algebra Ω. Then, we reduce the derivation of Ω to a certain form. With the reduced derivation and a torus of Ω, we determine the derivation algebra of Ω.
基金supported by the National Natural Science Foundation of China(No.11371182)the PhD Start-up Foundation of Liaoning University of China(No.2012002)the Predeclaration Fund of State Project of Liaoning University(No.2014LDGY01)
文摘The authors consider a family of finite-dimensional Lie superalgebras of C-type over an algebraically closed field of characteristic p 〉 3. It is proved that the Lie superalgebras of C-type are simple and the spanning sets are determined. Then the spanning sets are employed to characterize the superderivation algebras of these Lie superalgebras. Finally, the associative forms are discussed and a comparison is made between these Lie superalgebras and other simple Lie superalgebras of Cartan type.
基金Foundation item： the National Natural Science Foundation of China （No. 10271076） the Educational Commission of Heilongjiang Province （No. 11523065） the Science Foundation for the Youth of Harbin College （No. HXKQ200704）.
文摘In this paper F always denotes a field of characteristic p 〉 2. We construct the finitedimensional modular Lie superalgebra W（m,n, l, t_） over a field F, define θ-type derivation and determine the derivation superalgebra of W（m, n, l, t_）.
基金supported by the National Natural Science Foundation of China(Nos.11171055,11471090)the Fundamental Research Funds for the Central University(No.14ZZ2221)+3 种基金the Jilin Provincial Natural Science Foundation of China(No.201115006)the Heilongjiang Provincial Natural Science Foundation of China(No.A201210)the Technology Program of Education Department of Heilongjiang Province(No.12531763)the Program for Young Teachers Scientific Research in Qiqihar University(No.2012K-M32)
文摘Let F be the underlying base field of characteristic p 〉 3 and denote by M the even part of the finite-dimensional simple modular Lie superalgebra M. In this paper, the generator sets of the Lie algebra M which will be heavily used to consider the derivation algebra Der（M） are given. Furthermore, the derivation algebra of M is determined by reducing derivations and a torus of M, i.e., Der（m）=ad（m） spanF{∏l ad （ξr＋1ξl）} spanF{adxi,ad（xiξ^v）∏ad（ξr＋1ξl）}. As a result, the derivation algebra of the even part of M does not equal the even part of the derivation superalgebra of M.
基金Supported by National Natural Science Foundation of China(Nos.11501274,11771069,and 12071405)NSF of Jilin Province(No.20170101048JC)+1 种基金the project of Education Department of Jilin Province(No.JJKH20180005K)the Science Research Project of Liaoning Provincial Education Department of China(No.L2015203).
文摘Let F be the underlying base field of characteristic p>3 and denote by Гo the even part of the finite-dimensional Lie superalgebra T.We give the generator sets of the Lie algebra Гo.Using certain properties of the canonical tori of Гo,we describe explicitly the derivation algebra of Гo.
基金This work is partially supported by the National Natural Science Foundation of China(Grant No.10671160)China Postdoctoral Science Foundation(Grant No.20060400107)
文摘The embedding theorem is established for Z-graded transitive modular Lie superalgebras g■■■(g-1)satisfying the conditions: (i)g0■■(g-1) and g0-module g-1 is isomorphic to the natural■(g-1)-module; (ii)dim g1=2/3n(2n^2+1),where n=1/2dim g-1. In particular,it is proved that the finite-dimensional simple modular Lie superalgebras satisfying the conditions above are isomorphic to the odd Hamiltonian superalgebras.The restricted Lie superalgebras are also considered.
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.
