Infinite-Dimensional Modular Lie Superalgebra Ω

All ad-nilpotent elements of the infinite-dimensional Lie superalgebra Ω over a field of positive characteristic are determined. The natural filtration of the Lie superalgebra Ω is proved to be invariant under automorphisms by characterizing ad-nilpotent elements. Then an intrinsic property is obtai...

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Main Authors: Xiaoning Xu, Bing Mu
Format: Article
Language:English
Published: Wiley 2013-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2013/923101
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author Xiaoning Xu
Bing Mu
author_facet Xiaoning Xu
Bing Mu
author_sort Xiaoning Xu
collection DOAJ
description All ad-nilpotent elements of the infinite-dimensional Lie superalgebra Ω over a field of positive characteristic are determined. The natural filtration of the Lie superalgebra Ω 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 Ω are intrinsic. Therefore, we classify the infinite-dimensional modular Lie superalgebra Ω in the sense of isomorphism.
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publishDate 2013-01-01
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series Abstract and Applied Analysis
spelling doaj-art-40d69a71aa30480583e081468f70e6312025-02-03T07:25:07ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/923101923101Infinite-Dimensional Modular Lie Superalgebra ΩXiaoning Xu0Bing Mu1School of Mathematics, Liaoning University, Shenyang 110036, ChinaSchool of Mathematics, Liaoning University, Shenyang 110036, ChinaAll ad-nilpotent elements of the infinite-dimensional Lie superalgebra Ω over a field of positive characteristic are determined. The natural filtration of the Lie superalgebra Ω 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 Ω are intrinsic. Therefore, we classify the infinite-dimensional modular Lie superalgebra Ω in the sense of isomorphism.http://dx.doi.org/10.1155/2013/923101
spellingShingle Xiaoning Xu
Bing Mu
Infinite-Dimensional Modular Lie Superalgebra Ω
Abstract and Applied Analysis
title Infinite-Dimensional Modular Lie Superalgebra Ω
title_full Infinite-Dimensional Modular Lie Superalgebra Ω
title_fullStr Infinite-Dimensional Modular Lie Superalgebra Ω
title_full_unstemmed Infinite-Dimensional Modular Lie Superalgebra Ω
title_short Infinite-Dimensional Modular Lie Superalgebra Ω
title_sort infinite dimensional modular lie superalgebra ω
url http://dx.doi.org/10.1155/2013/923101
work_keys_str_mv AT xiaoningxu infinitedimensionalmodularliesuperalgebraō
AT bingmu infinitedimensionalmodularliesuperalgebraō