| Title:
|
Bicrossproduct Hopf quasigroups (English) |
| Author:
|
Klim, Jennifer |
| Author:
|
Majid, Shahn |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
51 |
| Issue:
|
2 |
| Year:
|
2010 |
| Pages:
|
287-304 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We recall the notion of Hopf quasigroups introduced previously by the authors. We construct a bicrossproduct Hopf quasigroup $kM {\triangleright\blacktriangleleft} k(G)$ from every group $X$ with a finite subgroup $G\subset X$ and IP quasigroup transversal $M\subset X$ subject to certain conditions. We identify the octonions quasigroup $G_{\mathbb O}$ as transversal in an order 128 group $X$ with subgroup $\mathbb Z_2^3$ and hence obtain a Hopf quasigroup $kG_{\mathbb O}{{>\blacktriangleleft}} k(\mathbb Z_2^3)$ as a particular case of our construction. (English) |
| Keyword:
|
IP loop |
| Keyword:
|
octonions |
| Keyword:
|
quantum group |
| Keyword:
|
quasiHopf algebra |
| Keyword:
|
monoidal category |
| Keyword:
|
finite group |
| Keyword:
|
coset |
| MSC:
|
16S36 |
| MSC:
|
16W50 |
| MSC:
|
81R50 |
| idZBL:
|
Zbl 1224.81014 |
| idMR:
|
MR2682482 |
| . |
| Date available:
|
2010-05-21T12:49:12Z |
| Last updated:
|
2014-07-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140108 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| . |
