Indecomposable set-theoretical solutions to the Quantum Yang-Baxter Equation on a set with prime number of elements

Simple item page
dc.creatorEtingof, Pavel
dc.creatorGuralnick, Robert
dc.creatorSoloviev, Alexander
dc.date2000-07-26
dc.date.accessioned2026-07-07T04:36:32Z
dc.date.available2026-07-07T04:36:32Z
dc.descriptionIn this paper we show that all indecomposable nondegenerate set-theoretical solutions to the Quantum Yang-Baxter equation on a set of prime order are affine, which allows us to give a complete and very simple classification of such solutions. This result is a natural application of the general theory of set-theoretical solutions to the quantum Yang-Baxter equation. It is also a generalization of the corresponding statement for involutive set-theoretical solutions proved in an earlier paper of P.E. and A.S. with T.Schedler. In order to prove our main result, we use the classification theory developed by the third author (based on the ideas of Lu, Yan, and Zhu) to reduce the problem to a group-theoretical statement: a finite group with trivial center generated by a conjugacy class of prime order is a subgroup of the affine group. Unfortunalely, we did not find an elementary proof of this statement, and our proof relies on the classification of outer automorphisms of finite simple groups.
dc.description9 pages, latex
dc.identifierhttps://arxiv.org/abs/math/0007170
dc.identifierhttp://arxiv.org/abs/math/0007170
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/59633
dc.subjectQuantum Algebra
dc.titleIndecomposable set-theoretical solutions to the Quantum Yang-Baxter Equation on a set with prime number of elements
dc.typetext

Files

Collections

arXiv