|
Organizers |
Zero-divisors and central elements in skein algebras
by
Adam S. Sikora
SUNY Buffalo
Coauthors: Jozef H. Prytycki
For a surface F, the space of links in F×[0,1] modulo Kauffman bracket skein relations is called the skein algebra of F, denoted by S(F). It is a non-commutative deformation of the SL(2,C)-character variety of F, of significant importance to quantum topology. In particular, for F with boundary, it is (almost) the quantum Teichmuller space of F.
Except for a few simplest surfaces F, not much is known about the algebraic properties of S(F) for closed F. We are going to prove the following two fundamental properties of skein algebras: 1. S(F) has no zero divisors, 2. Away from roots of unity, the center of S(F) is composed of polynomials in knots parallel to boundary components of F. This is joint work with J. H. Przytycki.
Date received: November 29, 2015
Copyright © 2015 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cblw-45.