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 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 paper, the derivation algebra of Lie superalgebra H of Caftan-type over F are determined by the calculating method in the situations of CharF = p ≥ 3 or m ≥ 2 or n ≥ 1. The main result is following： DerFH ...In this paper, the derivation algebra of Lie superalgebra H of Caftan-type over F are determined by the calculating method in the situations of CharF = p ≥ 3 or m ≥ 2 or n ≥ 1. The main result is following： DerFH = adH（H＂ ＋ Fh） （{（adDi）^pt ｜ i = 1,2,…,m, t=1,2,…,ti-1}）.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
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
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
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
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.
The main result of this paper is that every derivation of the finite-dimensional simple modular Lie superalgebra S（n） is inner, and S（n） has no nonsingular associative form.
We study class of finite-dimensional Cantan-type Lie superalgebras HO（m） over a field of prime characteristic, which can be regarded as extensions of odd Hamiltonian superalgebra HO. And we also determine the deriva...We study class of finite-dimensional Cantan-type Lie superalgebras HO（m） over a field of prime characteristic, which can be regarded as extensions of odd Hamiltonian superalgebra HO. And we also determine the derivation superalgebras of Lie superalgebras HO（m）.展开更多
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Supported by the Natural Science Foundation of the Henan Institute of Science and Technology（06057）
文摘In this paper, the derivation algebra of Lie superalgebra H of Caftan-type over F are determined by the calculating method in the situations of CharF = p ≥ 3 or m ≥ 2 or n ≥ 1. The main result is following： DerFH = adH（H＂ ＋ Fh） （{（adDi）^pt ｜ i = 1,2,…,m, t=1,2,…,ti-1}）.
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.
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Supported by the Tianyuan Fund for Mathematics （No. 11126051）, the Heilongjiang Provincial Natural Science Foundation of China （No. A201008）, the Scientific Research Fund of Heilongjiang Provincial Education Department （No. 12511157）, and the Doctoral Fund of Harbin Normal University （No. KJB201105）. This paper was completed when the second author visited the College of William and Mary, and he thanks the university and Professor Junping Shi for warm hospitality.
文摘The main result of this paper is that every derivation of the finite-dimensional simple modular Lie superalgebra S（n） is inner, and S（n） has no nonsingular associative form.
基金Acknowledgements The first author was supported by the National Natural Science Foundation of China （Grant No. 11301356）. The second author was supported by the Program for New Century Excellent Talents in Heilongjiang Provincial University （Grant No. 1254-NCET-010）.
文摘We study class of finite-dimensional Cantan-type Lie superalgebras HO（m） over a field of prime characteristic, which can be regarded as extensions of odd Hamiltonian superalgebra HO. And we also determine the derivation superalgebras of Lie superalgebras HO（m）.
