Special biserial algebras with no outer derivations

Ibrahim Assem, Juan Carlos Bustamante, and Patrick Le Meur. "Special biserial algebras with no outer derivations." Colloquium Mathematicae 125.1 (2011): 83-98. <http://eudml.org/doc/284117>.

@article{IbrahimAssem2011,
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.},
author = {Ibrahim Assem, Juan Carlos Bustamante, Patrick Le Meur},
journal = {Colloquium Mathematicae},
keywords = {special biserial algebras; path algebras; representation-finite algebras; Hochschild cohomology groups; simple connectedness; fundamental groups; projective-injective modules},
language = {eng},
number = {1},
pages = {83-98},
title = {Special biserial algebras with no outer derivations},
url = {http://eudml.org/doc/284117},
volume = {125},
year = {2011},
}

TY - JOUR
AU - Ibrahim Assem
AU - Juan Carlos Bustamante
AU - Patrick Le Meur
TI - Special biserial algebras with no outer derivations
JO - Colloquium Mathematicae
PY - 2011
VL - 125
IS - 1
SP - 83
EP - 98
AB - 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.
LA - eng
KW - special biserial algebras; path algebras; representation-finite algebras; Hochschild cohomology groups; simple connectedness; fundamental groups; projective-injective modules
UR - http://eudml.org/doc/284117
ER -