Special biserial algebras with no outer derivations

• Autorzy: Ibrahim Assem , Juan Carlos Bustamante , Patrick Le Meur
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 16G60: Representation type (finite, tame, wild, etc.)
• 16E40: (Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2011
• Tom: 125
• Numer: 1
• Strony: 83-98

Daty

wydano

2011

Twórcy

autor

Ibrahim Assem

• Département de Mathématiques, Université de Sherbrooke, Sherbrooke, Québec, Canada J1K 2R1

autor

Juan Carlos Bustamante

• Departamento de Matemáticas, Universidad San Fransisco de Quito, Cumbayá - Quito, Ecuador
• Département de Mathématiques, Université de Sherbrooke, Sherbrooke, Québec, Canada J1K 2R1

autor

Patrick Le Meur

• Laboratoire de Mathématiques, Université Blaise Pascal & CNRS, Campus Scientifique des Cézeaux, BP 80026, 63171 Aubière Cedex, France

Identyfikatory

DOI

10.4064/cm125-1-6