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Special biserial algebras with no outer derivations

Authors :
Assem, Ibrahim
Bustamante, Juan Carlos
Meur, Patrick Le
Source :
Colloquium Mathematicum 125(2011), 83-98
Publication Year :
2011

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.<br />Comment: 13 pages, submitted

Details

Database :
arXiv
Journal :
Colloquium Mathematicum 125(2011), 83-98
Publication Type :
Report
Accession number :
edsarx.1107.5099
Document Type :
Working Paper
Full Text :
https://doi.org/10.4064/cm125-1-6