On set-theoretical solutions of the quantum Yang-Baxter equation
| dc.creator | Etingof, Pavel | |
| dc.creator | Schedler, Travis | |
| dc.creator | Soloviev, Alexandre | |
| dc.date | 1997-07-22 | |
| dc.date | 1997-07-23 | |
| dc.date.accessioned | 2026-07-07T09:08:49Z | |
| dc.date.available | 2026-07-07T09:08:49Z | |
| dc.description | Recently V.Drinfeld formulated a number of problems in quantum group theory. In particular, he suggested to consider ``set-theoretical'' solutions of the quantum Yang-Baxter equation, i.e. solutions given by a permutation $R$ of the set $X\times X$, where $X$ is a fixed finite set. In this note we study such solutions, which satisfy the unitarity and the crossing symmetry conditions -- natural conditions arising in physical applications. More specifically, we consider ``linear'' solutions: the set $X$ is an abelian group, and the map $R$ is an automorphism of $X\times X$. We show that in this case, solutions are in 1-1 correspondence with pairs $a,b\in \End X$, such that $b$ is invertible and $bab^{-1}=\frac{a}{a+1}$. Later we consider ``affine'' solutions ($R$ is an automorphism of $X\times X$ as a principal homogeneous space), and show that they have a similar classification. The fact that these classifications are so nice leads us to think that there should be some interesting structure hidden behind this problem. | |
| dc.description | 4 pages, amstex; in the revised version there are minor changes; in particular, the set X is assumed to be finite | |
| dc.identifier | https://arxiv.org/abs/q-alg/9707027 | |
| dc.identifier | http://arxiv.org/abs/q-alg/9707027 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/150861 | |
| dc.subject | Quantum Algebra | |
| dc.title | On set-theoretical solutions of the quantum Yang-Baxter equation | |
| dc.type | text |