On Ternary Quotients of Cubic Hecke Algebras

TL;DR

This paper investigates quotients of the braid group algebra, showing collapse in most characteristics and defining new quotients with symmetry in characteristic 2, connecting to classical Hecke and BMW quotients.

Contribution

It proves collapse of certain braid group algebra quotients in non-characteristic 2 fields and introduces new quotients with order 3 symmetry in characteristic 2, linking to known algebraic structures.

Findings

Quotients collapse in characteristic not 2

New quotients with order 3 symmetry in characteristic 2

Conditions for Markov traces on these quotients

Abstract

We prove that the quotients of the group algebra of the braid group introduced by L. Funar in Comm. Math. Phys., 1995, collapses in characteristic distinct from 2. In characteristic 2 we define several quotients of it, which are connected to the classical Hecke and Birman-Wenzl-Murakami quotients, but which admit in addition a symmetry of order 3. We also establish conditions on the possible Markov traces factorizing through it.