scholarly journals Representations of Lie superalgebras in prime characteristic I

2009 ◽  
Vol 99 (1) ◽  
pp. 145-167 ◽  
Author(s):  
Weiqiang Wang ◽  
Lei Zhao
Keyword(s):  
Lie Superalgebras ◽  
Prime Characteristic

Special odd Lie superalgebras in prime characteristic

2011 ◽  
Vol 55 (3) ◽  
pp. 567-576 ◽  
Author(s):  
WenDe Liu ◽  
JiXia Yuan
Keyword(s):  
Lie Superalgebras ◽  
Prime Characteristic

scholarly journals Simple Modules for Modular Lie SuperalgebrasW(0∣n),S(0∣n), andK(n)

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Zhu Wei ◽  
Qingcheng Zhang ◽  
Yongzheng Zhang ◽  
Chunyue Wang
Keyword(s):  
Positive Root ◽  
Sufficient Conditions ◽  
Lie Superalgebras ◽  
Prime Characteristic ◽  
Simple Modules ◽  
Cartan Subalgebras ◽  
Modular Lie Superalgebras

This paper constructs a series of modules from modular Lie superalgebrasW(0∣n),S(0∣n), andK(n)over a field of prime characteristicp≠2. Cartan subalgebras, maximal vectors of these modular Lie superalgebras, can be solved. With certain properties of the positive root vectors, we obtain that the sufficient conditions of these modules are irreducibleL-modules, whereL=W(0∣n),S(0∣n), andK(n).

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.

FINITE-DIMENSIONAL SPECIAL ODD HAMILTONIAN SUPERALGEBRAS IN PRIME CHARACTERISTIC

2009 ◽  
Vol 11 (04) ◽  
pp. 523-546 ◽  
Author(s):  
WENDE LIU ◽  
YINGHUA HE
Keyword(s):  
Lie Superalgebras ◽  
The Other ◽  
Prime Characteristic ◽  
Characteristic P ◽  
Cartan Type ◽  
New Family ◽  
Finite Dimensional ◽  
Modular Lie Superalgebras

In this paper, we study a new family of finite-dimensional simple Lie superalgebras of Cartan type over a field of characteristic p > 3, the so-called special odd Hamiltonian superalgebras. The spanning sets are first given and then the grading structures are described explicitly. Finally, the simplicity and the dimension formulas are determined. As application, using the dimension formulas, we make a comparison between the special odd Hamiltonian superalgebras and the other known families of finite-dimensional simple modular Lie superalgebras of Cartan type.

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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