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Derivations for even part of finite-dimensional modular lie superalgebra Ω

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Frontiers of Mathematics in China 2012年第6期7卷 1169-1194页

作者： Zhu WEI Yongzheng ZHANG School of Mathematics and Statistics Northeast Normal University Changchun 130024 China

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.

关键词： modular lie superalgebra derivation algebra torus

The Even Part of Finite-Dimensional modular lie superalgebra Г

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Algebra Colloquium 2021年第3期28卷 479-496页

作者： Yusi Fan Xiaoning Xu Liangyun Chen School of Mathematics Northeast Normal University Changchun 130000China School of Mathematics Liaoning UniversityShenyang 110036China

Let F be the underlying base field of characteristic p>3 and denote by Гo the even part of the finite-dimensional lie superalgebra *** give the generator sets of the lie algebra Г*** certain properties of the canoni... 详细信息

关键词： modular lie superalgebra generator derivation

θ-Type Derivation and Derivation superalgebra of the Finite-Dimensional modular lie superalgebra W（m, n, l, t_）

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Journal of Mathematical Research and Exposition 2008年第2期28卷 297-304页

作者： FANG Xiao Chao ZHANG Yong Zheng Department of Mathematics Harbin College Heilongjiang 150080 China Department of Mathematics Northeast Normal University Jilin 130024 China

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... 详细信息

关键词： modular lie superalgebra generator derivation.

modular lie superalgebras of H-type

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Acta Mathematica Sinica,English Series 2004年第4期20卷 683-694页

作者： YongZhengZHANG DepartmentofMathematics HarbinNormalUniversityHarbin150080P.R.China

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.

关键词： modular lie superalgebra Divided power algebra Exterior algebra Flag

modular lie superalgebras of H-type

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Acta Mathematicae Applicatae Sinica 2004年第4期 683-694页

作者： Yong Zheng ZHANG Department of Mathematics,Harbin Normal University,Harbin 150080,P.R.China

In this article the Z-graded transitive modular lie superalgebra -1 Li,whose repre-sentation of Lin Lis isomorphic to the natural representation of osp(L),is determined.

关键词： modular lie superalgebra Divided power algebra Exterior algebra Flag

Restricted Envelopes of lie superalgebrast

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Algebra Colloquium 2015年第2期22卷 309-320页

作者： Liping Sun Wende Liu Xiaocheng Gao Boying Wu Department of Mathematics Harbin Institute of Technology Harbin 150006 China School of Mathematical Science Harbin Normal University Harbin 150025 China

Certain important results concerning p-envelopes of modular lie algebras are generalized to the super-case. In particular, any p-envelope of the lie algebra of a lie superalgebra can be naturally extended to a restricted envelope of the lie superalgebra. As an application, a theorem on the representations of lie superalgebras is given, which is a super-version of Iwasawa＇s theorem in lie algebra case. As an example, the minimal restricted envelopes are computed for three series of modular lie superalgebras of Cartan type.

关键词： modular lie superalgebra restricted envelope

A class of generalized odd HamUtonian lie superalgebras

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Frontiers of Mathematics in China 2014年第5期9卷 1105-1129页

作者： Li REN Qiang MU Yongzheng ZHANG School of Mathematics Sichuan University Chengdu 610064 China School of Mathematical Sciences Harbin Normal University Harbin 150025 China School of Mathematics and Statistics Northeast Normal University Changchun 130024 China

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... 详细信息

关键词： Derivation superalgebra modular lie superalgebra lie superalgebra of Cartan type

A Note on the Cartan Type lie superalgebra S（n） over a Field of Positive Characteristic

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Algebra Colloquium 2014年第3期21卷 521-526页

作者： Li Ren Qiang Mu Mathematical College Sichuan University Chengdu 610064 China School of Mathematical Sciences Harbin Normal University Harbin 150025 China

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.

关键词： modular lie superalgebra simple lie superalgebra derivation associativeform