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

Zhu Wei,Qingcheng Zhang,Yongzheng Zhang,Chunyue Wang

doi:10.1155/2015/250570

Abstract

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).

Highlights

Giving a broad overview of the present situation, the representation theories of Lie algebras and Lie superalgebras over a field of characteristic 0 have been a remarkable evolution
This paper constructs a series of modules from modular Lie superalgebras W(0 | n), S(0 | n), and K(n) over a field of prime characteristic p ≠ 2
The complete proof of the recognition theorem for graded Lie algebras in prime characteristic was given

Summary

Introduction

Giving a broad overview of the present situation, the representation theories of Lie algebras and Lie superalgebras over a field of characteristic 0 have been a remarkable evolution. This paper constructs a series of modules from modular Lie superalgebras W(0 | n), S(0 | n), and K(n) over a field of prime characteristic p ≠ 2. Maximal vectors of these modular Lie superalgebras, can be solved. More detailed description of one of the five simple exceptional Lie superalgebras of vector fields was given (see [3]).

Results

Conclusion