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Symmetric Hochschild extension algebras

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Ohnuki Y., Takeda K., Yamagata K.

Colloquium Mathematicum

1999

tom 80

nr 2

155-174

By an extension algebra of a finite-dimensional K-algebra A we mean a Hochschild extension algebra of A by the dual A-bimodule $Hom_K(A,K)$. We study the problem of when extension algebras of a K-algebra A are symmetric. (1) For an algebra A= KQ/I with an arbitrary finite quiver Q, we show a sufficient condition in terms of a 2-cocycle for an extension algebra to be symmetric. (2) Let L be a finite extension field of K. By using a given 2-cocycle of the K-algebra L, we construct a 2-cocycle of the K-algebra LQ for an arbitrary finite quiver Q without oriented cycles. Then we show a criterion on L for all those K-algebras LQ to have symmetric non-splittable extension algebras defined by the 2-cocycles.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Ohnuki Y.

1 Takeda K.

1 Yamagata K.

1 1999

Wyniki wyszukiwania

Symmetric Hochschild extension algebras