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

Qiaoling Xin; Lining Jiang; Zhenhua Ma

Czechoslovak Mathematical Journal (2015)

  • Volume: 65, Issue: 2, page 347-359
  • ISSN: 0011-4642

Abstract

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Let be a finite group and a subgroup. Denote by (or ) the crossed product of and (or ) with respect to the adjoint action of the latter on the former. Consider the algebra generated by and , where we regard as an idempotent operator on for a certain conditional expectation of onto . Let us call the basic construction from the conditional expectation . The paper constructs a crossed product algebra , and proves that there is an algebra isomorphism between and .

How to cite

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Xin, Qiaoling, Jiang, Lining, and Ma, Zhenhua. "The basic construction from the conditional expectation on the quantum double of a finite group." Czechoslovak Mathematical Journal 65.2 (2015): 347-359. <http://eudml.org/doc/270102>.

@article{Xin2015,
abstract = {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 $\mathbb \{C\}H$ (or $\mathbb \{C\}G$) 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 $C(G/H\times G)\rtimes \mathbb \{C\}G$, and proves that there is an algebra isomorphism between $\langle D(G),e\rangle $ and $C(G/H\times G)\rtimes \mathbb \{C\}G$.},
author = {Xin, Qiaoling, Jiang, Lining, Ma, Zhenhua},
journal = {Czechoslovak Mathematical Journal},
keywords = {conditional expectation; basic construction; quantum double; quasi-basis},
language = {eng},
number = {2},
pages = {347-359},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The basic construction from the conditional expectation on the quantum double of a finite group},
url = {http://eudml.org/doc/270102},
volume = {65},
year = {2015},
}

TY - JOUR
AU - Xin, Qiaoling
AU - Jiang, Lining
AU - Ma, Zhenhua
TI - The basic construction from the conditional expectation on the quantum double of a finite group
JO - Czechoslovak Mathematical Journal
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 65
IS - 2
SP - 347
EP - 359
AB - 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 $\mathbb {C}H$ (or $\mathbb {C}G$) 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 $C(G/H\times G)\rtimes \mathbb {C}G$, and proves that there is an algebra isomorphism between $\langle D(G),e\rangle $ and $C(G/H\times G)\rtimes \mathbb {C}G$.
LA - eng
KW - conditional expectation; basic construction; quantum double; quasi-basis
UR - http://eudml.org/doc/270102
ER -

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