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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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National Academy of Science of Ukraine
2009-12-01
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.3842/SIGMA.2009.108 |
| _version_ | 1819132211913293824 |
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| author | Tomoki Nakanishi Junji Suzuki Atsuo Kuniba |
| author_facet | Tomoki Nakanishi Junji Suzuki Atsuo Kuniba |
| author_sort | Tomoki Nakanishi |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-12-22T09:27:48Z |
| format | Article |
| id | doaj.art-9dc24876564e48ecb1f562ec6834f639 |
| institution | Directory Open Access Journal |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2024-12-22T09:27:48Z |
| publishDate | 2009-12-01 |
| publisher | National Academy of Science of Ukraine |
| record_format | Article |
| series | Symmetry, Integrability and Geometry: Methods and Applications |
| spelling | doaj.art-9dc24876564e48ecb1f562ec6834f6392022-12-21T18:31:02ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592009-12-015108T-Systems and Y-Systems for Quantum Affinizations of Quantum Kac-Moody AlgebrasTomoki NakanishiJunji SuzukiAtsuo KunibaThe 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.http://dx.doi.org/10.3842/SIGMA.2009.108T-systemsY-systemsquantum groupscluster algebras |
| spellingShingle | Tomoki Nakanishi Junji Suzuki Atsuo Kuniba T-Systems and Y-Systems for Quantum Affinizations of Quantum Kac-Moody Algebras Symmetry, Integrability and Geometry: Methods and Applications T-systems Y-systems quantum groups cluster algebras |
| 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 |
| topic | T-systems Y-systems quantum groups cluster algebras |
| url | http://dx.doi.org/10.3842/SIGMA.2009.108 |
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