Abstract
This paper is concerned with the completion of the proof of the Bergman centralizer theorem using generic matrices based on our previous quantization proof (Kanel-Belov et al. in Commun Algebra 46:2123–2129, 2018). Additionally, we establish that the algebra of generic matrices with characteristic coefficients is integrally closed.
| Original language | English |
|---|---|
| Article number | 85 |
| Journal | Mediterranean Journal of Mathematics |
| Volume | 20 |
| Issue number | 2 |
| DOIs | |
| State | Published - Apr 2023 |
Bibliographical note
Publisher Copyright:© 2023, The Author(s), under exclusive licence to Springer Nature Switzerland AG.
Funding
This work is a continuation of our work which has been carried out in [] by A. Belov-Kanel, F. Razavinia and W. Zhang. These authors contributed equally to this work. We thank U. Vishne and L. Rowen for useful discussions and we sincerely thank A. Elishev for revising our writing and providing rich discussions. We also thank the anonymous referee for valuable comments improving our manuscript. Alexei Belov-Kanel was supported by the Russian Science Foundation (Grant no. 22-11-00177). Wenchao Zhang was supported by the GuangDong Basic and Applied Basic Research Foundation (Grant no. 2022A1515110634), the Guangdong Provincial Department of Education (Grant no. 2021ZDJS080), and the Professorial and Doctoral Scientific Research Foundation of Huizhou University (Grant no. 2021JB022). Farrokh Razavinia was partially supported and funded by the science foundation of Azerbaijan Shahid Madani University.
| Funders | Funder number |
|---|---|
| Azarbaijan Shahid Madani University | |
| Huizhou University | 2021JB022 |
| Russian Science Foundation | 22-11-00177 |
| Department of Education of Guangdong Province | 2021ZDJS080 |
| Basic and Applied Basic Research Foundation of Guangdong Province | 2022A1515110634 |
Keywords
- Bergman centralizer theorem
- Deformation quantization
- free associative algebra
- generic matrices
- trace algebra