Set-theoretical solutions to the quantum Yang-Baxter equation
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
1998
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| _version_ | 1866915626990174208 |
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| author | Etingof, Pavel Schedler, Travis Soloviev, Alexandre |
| author_facet | Etingof, Pavel Schedler, Travis Soloviev, Alexandre |
| contents | In 1992 V$.$Drinfeld formulated a number of problems in quantum group theory. In particular, he suggested to consider ``set-theoretical'' solutions to the quantum Yang-Baxter equation, i.e. solutions given by a permutation R of the set $X\times X$, where X is a fixed set. In this paper we study such solutions, which in addition satisfy the unitarity and nondegeneracy conditions. We discuss the geometric and algebraic interpretations of such solutions, introduce several constructions of them, and make first steps towards their classification. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_9801047 |
| institution | arXiv |
| publishDate | 1998 |
| record_format | arxiv |
| spellingShingle | Set-theoretical solutions to the quantum Yang-Baxter equation Etingof, Pavel Schedler, Travis Soloviev, Alexandre Quantum Algebra In 1992 V$.$Drinfeld formulated a number of problems in quantum group theory. In particular, he suggested to consider ``set-theoretical'' solutions to the quantum Yang-Baxter equation, i.e. solutions given by a permutation R of the set $X\times X$, where X is a fixed set. In this paper we study such solutions, which in addition satisfy the unitarity and nondegeneracy conditions. We discuss the geometric and algebraic interpretations of such solutions, introduce several constructions of them, and make first steps towards their classification. |
| title | Set-theoretical solutions to the quantum Yang-Baxter equation |
| topic | Quantum Algebra |
| url | https://arxiv.org/abs/math/9801047 |