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arXiv · 1107.5099

Special biserial algebras with no outer derivations

Ibrahim Assem·Juan Carlos Bustamante·Patrick Le Meur
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Abstract

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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Ibrahim Assem, Juan Carlos Bustamante, Patrick Le Meur. 2011-07-26. Special biserial algebras with no outer derivations. https://doi.org/10.4064/cm125-1-6

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