The basic construction from the conditional expectation on the quantum double of a finite group

Czechoslovak Mathematical Journal

Qiaoling ¹  Xin² 

[1] Lining Jiang, School of Mathematics and Statistics, Beijing Institute of Technology, Higher Education Park, Liangxiang, Fangshan District, Beijing, 100081, P. R. China;School of Mathematics and Statistics, Beijing Institute of Technology, Higher Education Park, Liangxiang, Fangshan District, Beijing, 100081, P. R. China, and Department of Mathematics and Physics, Institute of Architecture Civil Engineering, No. 13, Chaoyang West Street, Zhangjiakou, Hebei, 075000, P. R. China

关键词: conditional expectation;    basic construction;    quantum double;    quasi-basis;   

DOI  :  

学科分类：数学（综合）

来源: Akademie Ved Ceske Republiky

【 摘 要 】

Let $G$ be a finite group and $H$ a subgroup. Denote by $D(G;H)$ (or $D(G)$) the crossed product of $C(G)$ and $\Bbb{C}H$ (or $\Bbb{C}G$) with respect to the adjoint action of the latter on the former. Consider the algebra $\langle D(G), e\rangle$ generated by $D(G)$ and $e$, where we regard $E$ as an idempotent operator $e$ on $D(G)$ for a certain conditional expectation $E$ of $D(G)$ onto $D(G;H)$. Let us call $\langle D(G), e\rangle$ the basic construction from the conditional expectation $ED(G)\rightarrow D(G;H)$. The paper constructs a crossed product algebra $C(G/H\times G)\rtimes\Bbb{C}G$, and proves that there is an algebra isomorphism between $\langle D(G),e\rangle$ and $C(G/H\times G)\rtimes\Bbb{C}G$.

【 授权许可】

Unknown