Special biserial algebras with no outer derivations
| Autor: | Assem, Ibrahim, Bustamante, Juan Carlos, Meur, Patrick Le |
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| Rok vydání: | 2011 |
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| Zdroj: | Colloquium Mathematicum 125(2011), 83-98 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.4064/cm125-1-6 |
| Popis: | Let $A$ be a special biserial algebra over an algebraically closed field. We show that the first Hohchshild cohomology group of $A$ with coefficients in the bimodule $A$ vanishes if and only if $A$ is representation finite and simply connected (in the sense of Bongartz and Gabriel), if and only if the Euler characteristic of $Q$ equals the number of indecomposable non uniserial projective injective $A$-modules (up to isomorphism). Moreover, if this is the case, then all the higher Hochschild cohomology groups of $A$ vanish. Comment: 13 pages, submitted |
| Databáze: | arXiv |
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