Canonical bimodules and dominant dimension
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- by Ming Fang, Otto Kerner and Kunio Yamagata PDF
- Trans. Amer. Math. Soc. 370 (2018), 847-872 Request permission
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 $A$.References
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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
- MR Author ID: 715486
- Email: fming@amss.ac.cn
- Otto Kerner
- Affiliation: Mathematisches Institut, Heinrich-Heine-Universität, 40225, Düsseldorf, Germany
- MR Author ID: 194039
- Email: kerner@math.uni-duesseldorf.de
- Kunio Yamagata
- Affiliation: Institute of Engineering, Tokyo University of Agriculture and Technology, Tokyo 184-8588, Japan
- MR Author ID: 226187
- Email: yamagata@cc.tuat.ac.jp
- 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)
- © Copyright 2017 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 370 (2018), 847-872
- MSC (2010): Primary 16D20, 16D40, 16D50, 16E10
- DOI: https://doi.org/10.1090/tran/6976
- MathSciNet review: 3729489
Dedicated: Dedicated to C. M. Ringel on the occasion of his 70th birthday