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Advances in Mathematical Physics
Volume 2015 (2015), Article ID 250570, 8 pages
http://dx.doi.org/10.1155/2015/250570
Research Article

Simple Modules for Modular Lie Superalgebras , , and

1School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China
2School of Applied Sciences, Jilin Teachers Institute of Engineering and Technology, Changchun 130052, China

Received 13 April 2015; Revised 28 June 2015; Accepted 30 June 2015

Academic Editor: Andrei D. Mironov

Copyright © 2015 Zhu Wei et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper constructs a series of modules from modular Lie superalgebras , , and over a field of prime characteristic . 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 irreducible -modules, where , , and .