ArticleOriginal scientific text

Title

Symmetric Hochschild extension algebras

Authors 1, 1, 2

Affiliations

  1. Institute of Mathematics, University of Tsukuba, 1-1-1 Tennodai, Tsukuba Ibaraki 305-0006, Japan
  2. Tokyo University of Agriculture and Technology, 3-5-8 Saiwaicho, Fuchu, Tokyo 183-0054, Japan

Abstract

By an extension algebra of a finite-dimensional K-algebra A we mean a Hochschild extension algebra of A by the dual A-bimodule HomK(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.

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Pages:
155-174
Main language of publication
English
Received
1998-08-05
Published
1999
Exact and natural sciences