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) and the 蔚 -exterior algebra 螞(V), and then establish an analogue of Chevalley identification between a667f1b52ed" title="Click to view the MathML source">C(V) and 螞(V). Secondly, we extend the non-degenerate bilinear form of degree zero on V to a non-degenerate bilinear form on 螞(V). Finally, as an application, we give a realization of the orthosymplectic 蔚-Lie algebra.