Article Dans Une Revue Colloquium Mathematicum Année : 2011

Special biserial algebras with no outer derivations

Résumé

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.

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Dates et versions

hal-00611234 , version 1 (25-07-2011)

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Ibrahim Assem, Juan Carlos Bustamante, Patrick Le Meur. Special biserial algebras with no outer derivations. Colloquium Mathematicum, 2011, 125 (1), pp.83-98. ⟨10.4064/cm125-1-6⟩. ⟨hal-00611234⟩
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