By an extension algebra of a finite-dimensional K-algebra A we mean a Hochschild extension algebra of A by the dual A-bimodule . 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.
@article{bwmeta1.element.bwnjournal-article-cmv80i2p155bwm,
author = {Yosuke Ohnuki and Kaoru Takeda and Kunio Yamagata},
title = {Symmetric Hochschild extension algebras},
journal = {Colloquium Mathematicae},
volume = {79},
year = {1999},
pages = {155-174},
zbl = {0961.16002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv80i2p155bwm}
}
Ohnuki, Yosuke; Takeda, Kaoru; Yamagata, Kunio. Symmetric Hochschild extension algebras. Colloquium Mathematicae, Tome 79 (1999) pp. 155-174. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv80i2p155bwm/
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