Manin Matrices for Quadratic Algebras
We give a general definition of Manin matrices for arbitrary quadratic algebras in terms of idempotents. We establish their main properties and give their interpretation in terms of category theory. The notion of minors is generalised for a general Manin matrix. We give some examples of Manin matric...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2021 |
| Main Author: | |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2021
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/211357 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Manin Matrices for Quadratic Algebras. Alexey Silantyev. SIGMA 17 (2021), 066, 81 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860124778983063552 |
|---|---|
| author | Silantyev, Alexey |
| author_facet | Silantyev, Alexey |
| citation_txt | Manin Matrices for Quadratic Algebras. Alexey Silantyev. SIGMA 17 (2021), 066, 81 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We give a general definition of Manin matrices for arbitrary quadratic algebras in terms of idempotents. We establish their main properties and give their interpretation in terms of category theory. The notion of minors is generalised for a general Manin matrix. We give some examples of Manin matrices, their relations with Lax operators, and obtain the formulae for some minors. In particular, we consider Manin matrices of the types , , and introduced by A. Molev and their relation with Brauer algebras. Infinite-dimensional Manin matrices and their connection with Lax operators are also considered.
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| first_indexed | 2026-03-19T20:47:06Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211357 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-19T20:47:06Z |
| publishDate | 2021 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Silantyev, Alexey 2025-12-30T15:55:10Z 2021 Manin Matrices for Quadratic Algebras. Alexey Silantyev. SIGMA 17 (2021), 066, 81 pages 1815-0659 2020 Mathematics Subject Classification: 16T99; 15B99 arXiv:2009.05993 https://nasplib.isofts.kiev.ua/handle/123456789/211357 https://doi.org/10.3842/SIGMA.2021.066 We give a general definition of Manin matrices for arbitrary quadratic algebras in terms of idempotents. We establish their main properties and give their interpretation in terms of category theory. The notion of minors is generalised for a general Manin matrix. We give some examples of Manin matrices, their relations with Lax operators, and obtain the formulae for some minors. In particular, we consider Manin matrices of the types , , and introduced by A. Molev and their relation with Brauer algebras. Infinite-dimensional Manin matrices and their connection with Lax operators are also considered. The author is grateful to A. Chervov, V. Rubtsov, An. Kirillov, A. Isaev, and A. Molev for useful discussions and advice. The author would like to thank anonymous referees for their attentive reading and numerous useful comments and remarks. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Manin Matrices for Quadratic Algebras Article published earlier |
| spellingShingle | Manin Matrices for Quadratic Algebras Silantyev, Alexey |
| title | Manin Matrices for Quadratic Algebras |
| title_full | Manin Matrices for Quadratic Algebras |
| title_fullStr | Manin Matrices for Quadratic Algebras |
| title_full_unstemmed | Manin Matrices for Quadratic Algebras |
| title_short | Manin Matrices for Quadratic Algebras |
| title_sort | manin matrices for quadratic algebras |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211357 |
| work_keys_str_mv | AT silantyevalexey maninmatricesforquadraticalgebras |