Adjoint Modules of Cartan Type Modular Lie Superalgebras W(n)

The classification of Cartan type modular Lie superalgebras is the key of the classification of Lie superalgebras over a fields of prime characteristic. The Recognition Theorem established foundation for the classification of Lie algebras over a fields of prime characteristic. According to the theor...

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Bibliographic Details
Main Authors: SUN Li-ping, ZHANG Qiu-yang, LIU Wen-de
Format: Article
Language:Chinese
Published: Harbin University of Science and Technology Publications 2021-12-01
Series:Journal of Harbin University of Science and Technology
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Online Access:https://hlgxb.hrbust.edu.cn/#/digest?ArticleID=2047
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Summary:The classification of Cartan type modular Lie superalgebras is the key of the classification of Lie superalgebras over a fields of prime characteristic. The Recognition Theorem established foundation for the classification of Lie algebras over a fields of prime characteristic. According to the theories on adjoint modules of Cartan type modular Lie algebras in Recognition Theorem, we study the adjoint modules of Cartan type modular Lie superalgebras W(n). By virtue of the direct sum decomposition of the Z2-graded components in W(n), we obtain two types of adjoint module, analyse the relationship between them, and prove their irreducibilities.
ISSN:1007-2683