Boundary Solutions of the Classical Yang-Baxter Equation
| dc.creator | Gerstenhaber, Murray | |
| dc.creator | Giaquinto, Anthony | |
| dc.date | 1996-09-16 | |
| dc.date.accessioned | 2026-07-07T09:17:15Z | |
| dc.date.available | 2026-07-07T09:17:15Z | |
| dc.description | We define a new class of unitary solutions to the classical Yang-Baxter equation (CYBE). These ``boundary solutions'' are those which lie in the closure of the space of unitary solutions to the modified classical Yang-Baxter equation (MCYBE). Using the Belavin-Drinfel'd classification of the solutions to the MCYBE, we are able to exhibit new families of solutions to the CYBE. In particular, using the Cremmer-Gervais solution to the MCYBE, we explicitly construct for all n > 2 a boundary solution based on the maximal parabolic subalgebra of sl(n) obtained by deleting the first negative root. We give some evidence for a generalization of this result pertaining to other maximal parabolic subalgebras whose omitted root is relatively prime to $n$. We also give examples of non-boundary solutions for the classical simple Lie algebras. | |
| dc.description | 21 pages, AMSTEX, A version of this report will appear in Lett. Math. Physics | |
| dc.identifier | https://arxiv.org/abs/q-alg/9609014 | |
| dc.identifier | http://arxiv.org/abs/q-alg/9609014 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/153602 | |
| dc.subject | Quantum Algebra | |
| dc.title | Boundary Solutions of the Classical Yang-Baxter Equation | |
| dc.type | text |