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Canonical bimodules and dominant dimension


Authors: Ming Fang, Otto Kerner and Kunio Yamagata
Journal: Trans. Amer. Math. Soc.
MSC (2010): Primary 16D20, 16D40, 16D50, 16E10
DOI: https://doi.org/10.1090/tran/6976
Published electronically: July 13, 2017
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Abstract: For a finite dimensional algebra $ A$ over a field $ k$, the inherent $ A$-bimodules which include $ A$ and its $ k$-dual $ \mathrm {D}(A)$, as well as those derived from them by iteratively taking their left or right $ A$-duals or higher extensions, are crucial in many considerations. We study the properties of these bimodules, mainly of $ \mathrm {Hom}_A(\mathrm {D}(A),A)$ (called the canonical $ A$-bimodule), and utilize them to provide new characterizations of Morita algebras and the dominant dimension of $ A$.


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Additional Information

Ming Fang
Affiliation: Academy of Mathematics and Systems Science, Chinese Academy of Sciences, 100190 – and – School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, People’s Republic of China
Email: fming@amss.ac.cn

Otto Kerner
Affiliation: Mathematisches Institut, Heinrich-Heine-Universität, 40225, Düsseldorf, Germany
Email: kerner@math.uni-duesseldorf.de

Kunio Yamagata
Affiliation: Institute of Engineering, Tokyo University of Agriculture and Technology, Tokyo 184-8588, Japan
Email: yamagata@cc.tuat.ac.jp

DOI: https://doi.org/10.1090/tran/6976
Keywords: Bimodule, dominant dimension, Morita algebra
Received by editor(s): May 28, 2015
Received by editor(s) in revised form: April 30, 2016
Published electronically: July 13, 2017
Additional Notes: The first-named author’s research was supported by Natural Science Foundation of China (No. 11271318 and No. 11471315). The third-named author’s research was supported by JSPS KAKENHI (No. 25400036 and No. 16K05091)
Dedicated: Dedicated to C. M. Ringel on the occasion of his 70th birthday
Article copyright: © Copyright 2017 American Mathematical Society