On the algebra structure of some bismash products
| Autor: | Clarke, Matthew C. |
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| Rok vydání: | 2011 |
| Předmět: | |
| Zdroj: | Journal of Algebra, Vol: 322, Issue: 7, Date: October 1, 2009, Pages: 2590-2600 |
| Druh dokumentu: | Working Paper |
| Popis: | We study several families of semisimple Hopf algebras, arising as bismash products, which are constructed from finite groups with a certain specified factorization. First we associate a bismash product $H_q$ of dimension $q(q-1)(q+1)$ to each of the finite groups $PGL_2(q)$ and show that these $H_q$ do not have the structure (as algebras) of group algebras (except when $q =2,3$). As a corollary, all Hopf algebras constructed from them by a comultiplication twist also have this property and are thus non-trivial. We also show that bismash products constructed from Frobenius groups do have the structure (as algebras) of group algebras. Comment: 11 pages |
| Databáze: | arXiv |
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