A+ CATEGORY SCIENTIFIC UNIT

Special biserial algebras with no outer derivations

Volume 125 / 2011

Ibrahim Assem, Juan Carlos Bustamante, Patrick Le Meur Colloquium Mathematicum 125 (2011), 83-98 MSC: Primary 16E40, 16G60. DOI: 10.4064/cm125-1-6

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.

Authors

  • Ibrahim AssemDépartement de Mathématiques
    Université de Sherbrooke
    Sherbrooke, Québec, Canada J1K 2R1
    e-mail
  • Juan Carlos BustamanteDepartamento de Matemáticas
    Universidad San Fransisco de Quito
    Cumbayá - Quito, Ecuador
    and
    Département de Mathématiques
    Université de Sherbrooke
    Sherbrooke, Québec, Canada J1K 2R1
    e-mail
  • Patrick Le MeurLaboratoire de Mathématiques
    Université Blaise Pascal & CNRS
    Campus Scientifique des Cézeaux
    BP 80026
    63171 Aubière Cedex, France
    e-mail

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