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Markov trace on cubic Hecke algebra
by
Stepan Orevkov
IMT, Universite Paul Sabatier, Toulouse France
Funar algebra K∞=K∞(α, β;k) is the quotient of the group algebra over a ring k of the braid group B∞ by two cubic relations: σ13−ασ12+βσ1−1=0 and another one which involves σ1 and σ2. The universal Markov trace on K∞ is the quotient map t of K∞(α, β, k[u, v]) to its quotient (as a k[u, v]-module) by trace relations xy=yx and by Markov relations σnx=ux, σn−1x=vx for x ∈ Kn. It is easy to check (due to the specific form of Funar's relation) that the quotient is of the form k[u, v]/I for some ideal I (i. e. that the trace t is determined by t(1)). We give an algorithm to compute the ideal I and we present the result of computations in some special cases. We also discuss how to define invariants of tranverse links using one-sided Markov trace on cubic Hecke algebras.
Date received: December 15, 2018
Copyright © 2018 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 # cbpq-28.