T-Systems and Y-Systems for Quantum Affinizations of Quantum Kac-Moody Algebras
The T-systems and Y-systems are classes of algebraic relations originally associated with quantum affine algebras and Yangians. Recently the T-systems were generalized to quantum affinizations of a wide class of quantum Kac-Moody algebras by Hernandez. In this note we introduce the corresponding Y-s...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2009 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2009
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/149098 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | T-Systems and Y-Systems for Quantum Affinizations of Quantum Kac-Moody Algebras / A. Kuniba, T. Nakanishi, J. Suzuki // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 58 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862722869877800960 |
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| author | Kuniba, A. Nakanishi, T. Suzuki, J. |
| author_facet | Kuniba, A. Nakanishi, T. Suzuki, J. |
| citation_txt | T-Systems and Y-Systems for Quantum Affinizations of Quantum Kac-Moody Algebras / A. Kuniba, T. Nakanishi, J. Suzuki // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 58 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | The T-systems and Y-systems are classes of algebraic relations originally associated with quantum affine algebras and Yangians. Recently the T-systems were generalized to quantum affinizations of a wide class of quantum Kac-Moody algebras by Hernandez. In this note we introduce the corresponding Y-systems and establish a relation between T and Y-systems. We also introduce the T and Y-systems associated with a class of cluster algebras, which include the former T and Y-systems of simply laced type as special cases.
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| first_indexed | 2025-12-07T18:39:02Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149098 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T18:39:02Z |
| publishDate | 2009 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Kuniba, A. Nakanishi, T. Suzuki, J. 2019-02-19T17:19:48Z 2019-02-19T17:19:48Z 2009 T-Systems and Y-Systems for Quantum Affinizations of Quantum Kac-Moody Algebras / A. Kuniba, T. Nakanishi, J. Suzuki // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 58 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 17B37; 13A99 https://nasplib.isofts.kiev.ua/handle/123456789/149098 The T-systems and Y-systems are classes of algebraic relations originally associated with quantum affine algebras and Yangians. Recently the T-systems were generalized to quantum affinizations of a wide class of quantum Kac-Moody algebras by Hernandez. In this note we introduce the corresponding Y-systems and establish a relation between T and Y-systems. We also introduce the T and Y-systems associated with a class of cluster algebras, which include the former T and Y-systems of simply laced type as special cases. It is our great pleasure to thank Professor Tetsuji Miwa on the occasion of his sixtieth birthday for his generous support and continuous interest in our works through many years. We also thank David Hernandez for a valuable comment. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications T-Systems and Y-Systems for Quantum Affinizations of Quantum Kac-Moody Algebras Article published earlier |
| spellingShingle | T-Systems and Y-Systems for Quantum Affinizations of Quantum Kac-Moody Algebras Kuniba, A. Nakanishi, T. Suzuki, J. |
| title | T-Systems and Y-Systems for Quantum Affinizations of Quantum Kac-Moody Algebras |
| title_full | T-Systems and Y-Systems for Quantum Affinizations of Quantum Kac-Moody Algebras |
| title_fullStr | T-Systems and Y-Systems for Quantum Affinizations of Quantum Kac-Moody Algebras |
| title_full_unstemmed | T-Systems and Y-Systems for Quantum Affinizations of Quantum Kac-Moody Algebras |
| title_short | T-Systems and Y-Systems for Quantum Affinizations of Quantum Kac-Moody Algebras |
| title_sort | t-systems and y-systems for quantum affinizations of quantum kac-moody algebras |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149098 |
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