Generalized Clifford theory for graded spaces

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• 作者：Zhiqi Chen^a ; ¹ ; ^{chenzhiqi@nankai.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Yifang Kang^b ; ² ; ^{kangyf@tju.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：15A66 ; 17B75
• 刊名：Journal of Pure and Applied Algebra
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：220
• 期：2
• 页码：647-665
• 全文大小：393 K

文摘

Assume that 螕 is a finite abelian group and 蔚 is an antisymmetric bicharacter on 螕. Let V be a 螕-graded space with a non-degenerate 蔚-symmetric bilinear form of degree zero. The goal of this paper is to develop a generalized Clifford theory on V. We first introduce the 蔚  -Clifford algebra a667f1b52ed" title="Click to view the MathML source">C(V)$C(V)$ and the 蔚  -exterior algebra 螞(V)$\mathrm{螞}(V)$, and then establish an analogue of Chevalley identification between a667f1b52ed" title="Click to view the MathML source">C(V)$C(V)$ and 螞(V)$\mathrm{螞}(V)$. Secondly, we extend the non-degenerate bilinear form of degree zero on V   to a non-degenerate bilinear form on 螞(V)$\mathrm{螞}(V)$. Finally, as an application, we give a realization of the orthosymplectic 蔚-Lie algebra.