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Special biserial algebras with no outer derivations

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Assem I., Bustamante J., Le Meur P.

Colloquium Mathematicum

2011

tom 125

nr 1

83-98

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.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Assem I.

1 Bustamante J.

1 Le Meur P.

1 2011

Wyniki wyszukiwania

Special biserial algebras with no outer derivations