Yang-Baxterization of the BH algebra

TL;DR

This paper introduces a Yang-Baxterization process for the BH algebra, deriving algebraic solutions to the Yang-Baxter equation that extend known solutions for the Birman-Wenzl algebra.

Contribution

It generalizes the Yang-Baxterization method to the BH algebra, providing explicit algebraic solutions that extend previous work on the Birman-Wenzl algebra.

Findings

Derived algebraic solutions to the Yang-Baxter equation for BH algebra

Extended known solutions from Birman-Wenzl algebra to BH algebra

Provided a generalized algebraic expression for the solutions

Abstract

The BH algebra is defined by two sets of generators one of which satisfy the relations of the braid group and the other the relations of the Hecke algebra of projectors.These algebras are then combined by additional relations in a way which generalizes the Birman-Wenzl algebra.In this paper we Yang-Baxterize the algebra BH and compute solutions of the Yang-Baxter equation.The solutions found are expressed algebraically in terms of the generators of the algebra.The expression generalizes the known one for the Birman-Wenzl algebra.