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Abstract and Applied Analysis
Volume 2013, Article ID 923101, 10 pages
http://dx.doi.org/10.1155/2013/923101
Research Article

Infinite-Dimensional Modular Lie Superalgebra

School of Mathematics, Liaoning University, Shenyang 110036, China

Received 2 July 2013; Accepted 28 July 2013

Academic Editor: Teoman Özer

Copyright © 2013 Xiaoning Xu and Bing Mu. 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

All ad-nilpotent elements of the infinite-dimensional Lie superalgebra over a field of positive characteristic are determined. The natural filtration of the Lie superalgebra is proved to be invariant under automorphisms by characterizing ad-nilpotent elements. Then an intrinsic property is obtained by the invariance of the filtration; that is, the integers in the definition of are intrinsic. Therefore, we classify the infinite-dimensional modular Lie superalgebra in the sense of isomorphism.