A bt-algebra of type B

TL;DR

This paper introduces a new algebraic structure called the bt-algebra of type B, providing foundational properties, representations, and link invariants relevant to knot theory in the solid torus.

Contribution

It constructs the first bt-algebra of type B, establishes a basis, a faithful tensorial representation, and demonstrates it supports a Markov trace for link invariants.

Findings

Established a basis for the bt-algebra of type B

Developed a faithful tensorial representation

Proved the algebra supports a Markov trace and derived link invariants

Abstract

We introduce a bt-algebra of type B. We define this algebra doing the natural analogy with the original construction of the bt-algebra. Notably we find a basis for it, a faithful tensorial representation, and we prove that it supports a Markov trace, from which we derive invariants of classical links in the solid torus.