Stable equivalence of Morita type and Frobenius extensions
| Autor: | Beattie, M., Caenepeel, S., Raianu, S. |
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| Rok vydání: | 2012 |
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| Druh dokumentu: | Working Paper |
| Popis: | A.S. Dugas and R. Mart\'{i}nez-Villa proved in \cite[Corollary 5.1]{dm} that if there exists a stable equivalence of Morita type between the $k$-algebras $\Lambda$ and $\Gamma$, then it is possible to replace $\Lambda$ by a Morita equivalent $k$-algebra $\Delta$ such that $\Gamma$ is a subring of $\Delta$ and the induction and restriction functors induce inverse stable equivalences. In this note we give an affirmative answer to a question of Alex Dugas about the existence of a $\Gamma$-coring structure on $\Delta$. We do this by showing that $\Delta$ is a Frobenius extension of $\Gamma$. Comment: 4 pages, to appear in Annals Univ. Bucharest |
| Databáze: | arXiv |
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