设kG是群代数, D(kG)是其量子偶.证明了D(kG)的表示环的结构可完全由群G的共轭类代表元的中心化子子群的表示环决定.作为该结论的应用我们给出了量子偶D(KDn)的表示环的结构,其中k是一个特征为2的域, n是奇数,Dn是2n阶二面体群.
Abstract
Let kG be a group algebra, and D(kG) the quantum double of kG. We first prove that the structure of representation ring of D(kG) can be described in terms of the representation ring of centralizer subgroups of representatives of conjugate classes of G. As an application, we then describe the structure of representation ring of D(kGn), where k is a field of characteristic 2, n is odd, and Dn is a dihedral group of order 2n.
关键词
表示环 /
量子偶 /
二面体群 /
Brauer特征标
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Key words
representation ring /
quantum double /
dihedral group /
Brauer character
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参考文献
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脚注
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基金
国家自然科学基金资助项目(11201231, 11171291);中国博士后基金资助项目(2012M511643);江苏省博士后基金资助项目(1102041C)
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