scholarly journals Constructions and Properties for a Finite-Dimensional Modular Lie Superalgebra K n , m

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Dan Mao ◽  
Keli Zheng
Keyword(s):  
Lie Superalgebra ◽  
Prime Characteristic ◽  
Modular Lie Superalgebra ◽  
Restricted Lie Superalgebra ◽  
Finite Dimensional

In this paper, a finite-dimensional Lie superalgebra K n , m over a field of prime characteristic is constructed. Then, we study some properties of K n , m . Moreover, we prove that K n , m is an extension of a simple Lie superalgebra, and if m = n − 1 , then it is isomorphic to a subalgebra of a restricted Lie superalgebra.

scholarly journals The Natural Filtration of Finite Dimensional Modular Lie Superalgebras of Special Type

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Keli Zheng ◽  
Yongzheng Zhang
Keyword(s):  
Lie Superalgebra ◽  
Lie Superalgebras ◽  
Prime Characteristic ◽  
Modular Lie Superalgebra ◽  
Finite Dimensional ◽  
Natural Filtration ◽  
Modular Lie Superalgebras

This paper is concerned with the natural filtration of Lie superalgebraS(n,m)of special type over a field of prime characteristic. We first construct the modular Lie superalgebraS(n,m). Then we prove that the natural filtration ofS(n,m)is invariant under its automorphisms.

The Finite-dimensional Modular Lie Superalgebra Γ

2010 ◽  
Vol 17 (03) ◽  
pp. 525-540 ◽  
Author(s):  
Xiaoning Xu ◽  
Yongzheng Zhang ◽  
Liangyun Chen
Keyword(s):  
Lie Superalgebra ◽  
Lie Superalgebras ◽  
Explicit Description ◽  
Cartan Type ◽  
Modular Lie Superalgebra ◽  
New Family ◽  
Finite Dimensional ◽  
Derivation Superalgebra ◽  
Modular Lie Superalgebras

A new family of finite-dimensional modular Lie superalgebras Γ is defined. The simplicity and generators of Γ are studied and an explicit description of the derivation superalgebra of Γ is given. Moreover, it is proved that Γ is not isomorphic to any known Lie superalgebra of Cartan type.

Second Cohomology of the Modular Lie Superalgebra of Cartan Type K

2009 ◽  
Vol 16 (02) ◽  
pp. 309-324 ◽  
Author(s):  
Wenjuan Xie ◽  
Yongzheng Zhang
Keyword(s):  
Cohomology Group ◽  
Lie Superalgebra ◽  
Closed Field ◽  
Algebraically Closed Field ◽  
Cartan Type ◽  
Modular Lie Superalgebra ◽  
Finite Dimensional ◽  
Type K

Let 𝔽 be an algebraically closed field and char 𝔽 = p > 3. In this paper, we determine the second cohomology group of the finite-dimensional Contact superalgebra K(m,n,t).

Finite-dimensional simple modular Lie superalgebra ℳ

2012 ◽  
Vol 8 (2) ◽  
pp. 411-441 ◽  
Author(s):  
Lili Ma ◽  
Liangyun Chen ◽  
Yongzheng Zhang
Keyword(s):  
Lie Superalgebra ◽  
Modular Lie Superalgebra ◽  
Finite Dimensional

scholarly journals The finite-dimensional modular Lie superalgebra Ω

2009 ◽  
Vol 321 (12) ◽  
pp. 3601-3619 ◽  
Author(s):  
Yongzheng Zhang ◽  
Qingcheng Zhang
Keyword(s):  
Lie Superalgebra ◽  
Modular Lie Superalgebra ◽  
Finite Dimensional

Automorphisms and p-Characters of Restricted Lie Superalgebras of Cartan Type

2011 ◽  
Vol 18 (03) ◽  
pp. 397-410 ◽  
Author(s):  
Jixia Yuan ◽  
Yan Chen ◽  
Wende Liu
Keyword(s):  
Automorphism Group ◽  
Lie Superalgebra ◽  
Lie Superalgebras ◽  
Irreducible Representations ◽  
Prime Characteristic ◽  
Cartan Type ◽  
Restricted Lie Superalgebra ◽  
Normal Series ◽  
Standard Normal

Let X be a restricted Lie superalgebra of Cartan type W, S, H or K over a field of prime characteristic. In this paper, we describe the quotients of the standard normal series of the automorphism group of X. As an application, the results above are used to discuss the p-characters of the irreducible representations for X.

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