Yang-Baxter deformations of quandles and racks

Details Yang-Baxter deformations of quandles and racks Yang-Baxter deformations of quandles and racks

2004-09-13

arxiv.org/abs/math/0409202v2

Algebr. Geom. Topol. 5 (2005) 537-562

Mathematics

Quantum Algebra

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-23.abs.html

Scientific paper

Given a rack Q and a ring A, one can construct a Yang-Baxter operator c_Q: V tensor V --> V tensor V on the free A-module V = AQ by setting c_Q(x tensor y) = y tensor x^y for all x,y in Q. In answer to a question initiated by D.N. Yetter and P.J. Freyd, this article classifies formal deformations of c_Q in the space of Yang-Baxter operators. For the trivial rack, where x^y = x for all x,y, one has, of course, the classical setting of r-matrices and quantum groups. In the general case we introduce and calculate the cohomology theory that classifies infinitesimal deformations of c_Q. In many cases this allows us to conclude that c_Q is rigid. In the remaining cases, where infinitesimal deformations are possible, we show that higher-order obstructions are the same as in the quantum case.

Affiliated with

Also associated with

No associations

Rating

Yang-Baxter deformations of quandles and racks does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Yang-Baxter deformations of quandles and racks, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Yang-Baxter deformations of quandles and racks will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-530833