Inductive basis on Birman-Murakami-Wenzl algebras and (transverse) Markov traces

TL;DR

This paper introduces a new inductive basis for BMW algebras, providing a novel proof of the Markov trace's existence and classifying all transverse Markov traces via key link invariants.

Contribution

It constructs an inductive basis for BMW algebras and characterizes all transverse Markov traces using classical link invariants.

Findings

New inductive basis for BMW algebras

Alternative proof of Markov trace existence

Classification of transverse Markov traces

Abstract

We construct a new inductive basis of the Birman-Murakami-Wenzl algebra. Using it, we provide a new proof of the existence of the Markov trace on the BMW algebras affording the two-variable Kauffman polynomial. We prove also that all the transverse Markov traces on the BMW algebras are determined by the self-linking number, the HOMFLY-PT polynomial and the two-variable Kauffman polynomial.