Geodesic
The basic construction from the conditional expectation on the quantum double of a finite group
Czechoslovak Mathematical Journal, Tome 65 (2015) no. 2, pp. 347-359.

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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 $E\colon D(G)\rightarrow D(G;H)$. 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 $C(G/H\times G)\rtimes \Bbb {C}G$.
DOI : 10.1007/s10587-015-0179-0
Classification : 16S35, 16S99, 16W22, 20D99
Keywords: conditional expectation; basic construction; quantum double; quasi-basis 
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     title = {The basic construction from the conditional expectation on the quantum double of a finite group},
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Xin, Qiaoling; Jiang, Lining; Ma, Zhenhua. The basic construction from the conditional expectation on the quantum double of a finite group. Czechoslovak Mathematical Journal, Tome 65 (2015) no. 2, pp. 347-359. doi : 10.1007/s10587-015-0179-0. http://geodesic.mathdoc.fr/articles/10.1007/s10587-015-0179-0/

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