A Framization of the Hecke algebra of Type B
Marcelo Flores, Jesus Juyumaya, Sofia Lambropoulou
TL;DR
This paper introduces a new algebraic structure called a framization of the Hecke algebra of type B, along with representations, bases, and invariants for knots and links in the solid torus.
Contribution
It presents the first framization of the Hecke algebra of type B, including faithful representations, bases, and knot invariants derived from a Markov trace.
Findings
Constructed a faithful tensorial representation.
Developed two linear bases for the algebra.
Derived isotopy invariants for knots and links.
Abstract
In this article we introduce a framization of the Hecke algebra of type B. For this framization we construct a faithful tensorial representation and two linear bases. We finally construct a Markov trace on these algebras and from this trace we derive isotopy invariants for framed and classical knots and links in the solid torus.
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