| Title:
|
The basic construction from the conditional expectation on the quantum double of a finite group (English) |
| Author:
|
Xin, Qiaoling |
| Author:
|
Jiang, Lining |
| Author:
|
Ma, Zhenhua |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
65 |
| Issue:
|
2 |
| Year:
|
2015 |
| Pages:
|
347-359 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $C(G/H\times G)\rtimes \Bbb {C}G$. (English) |
| Keyword:
|
conditional expectation |
| Keyword:
|
basic construction |
| Keyword:
|
quantum double |
| Keyword:
|
quasi-basis |
| MSC:
|
16S35 |
| MSC:
|
16S99 |
| MSC:
|
16W22 |
| MSC:
|
20D99 |
| idZBL:
|
Zbl 06486950 |
| idMR:
|
MR3360430 |
| DOI:
|
10.1007/s10587-015-0179-0 |
| . |
| Date available:
|
2015-06-16T17:40:58Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144273 |
| . |
| Reference:
|
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