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Gendo-symmetric algebras, canonical comultiplication, bar cocomplex and dominant dimension

Authors: Ming Fang and Steffen Koenig
Journal: Trans. Amer. Math. Soc. 368 (2016), 5037-5055
MSC (2010): Primary 16G10, 13E10
Published electronically: October 5, 2015
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Abstract: To each endomorphism algebra $ A$ of a generator over a symmetric algebra, first a canonical comultiplication (possibly without a counit) is constructed and then a bar cocomplex. The algebras $ A$ are characterised by the existence of this data. The dominant dimension of $ A$ is shown to be determined by the exactness of the cocomplex at its beginning terms.

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Additional Information

Ming Fang
Affiliation: Institute of Mathematics, Chinese Academy of Sciences Beijing 100190, People’s Republic of China

Steffen Koenig
Affiliation: Institute of Algebra and Number Theory, University of Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany

Keywords: Endomorphism algebra, bar cocomplex, dominant dimension
Received by editor(s): January 22, 2014
Received by editor(s) in revised form: June 4, 2014
Published electronically: October 5, 2015
Additional Notes: The first author was supported by the National Natural Science Foundation of China (No.11001253 and No. 11271318)
Article copyright: © Copyright 2015 American Mathematical Society