Trigonometric solutions of the associative Yang-Baxter equation
| dc.creator | Schedler, Travis | |
| dc.date | 2002-12-18 | |
| dc.date | 2003-03-26 | |
| dc.date.accessioned | 2026-07-07T04:53:54Z | |
| dc.date.available | 2026-07-07T04:53:54Z | |
| dc.description | We classify trigonometric solutions to the associative Yang-Baxter equation (AYBE) for A = Mat_n, the associative algebra of n-by-n matrices. The AYBE was first presented in a 2000 article by Marcelo Aguiar and also independently by Alexandre Polishchuk. Trigonometric AYBE solutions limit to solutions of the classical Yang-Baxter equation. We find that such solutions of the AYBE are equal to special solutions of the quantum Yang-Baxter equation (QYBE) classified by Gerstenhaber, Giaquinto, and Schack (GGS), divided by a factor of q - q^{-1}, where q is the deformation parameter q = exp(h). In other words, when it exists, the associative lift of the classical r-matrix coincides with the quantum lift up to a factor. We give explicit conditions under which the associative lift exists, in terms of the combinatorial classification of classical r-matrices through Belavin-Drinfeld triples. The results of this paper illustrate nontrivial connections between the AYBE and both classical (Lie) and quantum bialgebras. | |
| dc.description | 20 pages, AMSLaTeX with BibTeX references and the MRL article class. v2 includes minor corrections | |
| dc.identifier | https://arxiv.org/abs/math/0212258 | |
| dc.identifier | http://arxiv.org/abs/math/0212258 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66033 | |
| dc.subject | Quantum Algebra | |
| dc.title | Trigonometric solutions of the associative Yang-Baxter equation | |
| dc.type | text |