On the quotients of cubic Hecke algebras

Abstract

Between the rank 3 quotients of cubic Hecke algebras there is essentially one of maximal dimension. We prove it has a unique Markov trace having values in a torsion module. Therefore the description of a Markov trace on the cubic Hecke algebra corresponding to x 3 -j-1 and having the parameters (1,1) is derived. Thus we obtain a numerical link invariant of finite degree, and define a whole sequence of 3 rd order Vassiliev invariants. Contents1. Introduction 513 2. The quotients of H(Q,3) 517 3. Markov traces on K^y) 524 4. Link groups and invariants 528 5. Graphical reduction of obstructions 533 A.

Universal deformations of the finite quotients of the braid group on 3 strands

“…For the finite quotients W k of the braid group we mentioned before, this conjecture is known to be true for the symmetric group (see [9], Lemma 4.4.3), and it was proved in [8], [2] and [15] for the case of G 4 and in [15] for the cases of G 25 and G 32 . We will prove the validity of the conjecture for the rest of the cases, which belong to the class of complex reflection groups of rank two 2 ; the main theorem of this paper is the following: Theorem 1.1.…”

Markov Traces on the Funar Algebra

“…. It is claimed in [3] and [1] that a nontrivial Markov trace is constructed on K n . About 2004-2005 I indicated a gap in the proof of its well-definedness (see Typeset by A M S-T E X 1 Remark 2.11 below).…”

A New Algebra From the Representation Theory of Finite Groups

“…, b n−1 . The cubic Hecke algebra was studied by L. Funar [7]. We use from [7] the following result:…”

“…For n = 2 it is trivial. For n = 3 it is a consequence of Lemma 2.4 [7], because the algebra J n (u) is a quotient of the cubic Hecke algebra.…”