On the framization of knot algebras

TL;DR

This paper explores the concept of framization in knot algebras, extending it to various algebraic structures like the BMW and Hecke algebras, motivated by Yokonuma--Hecke algebras.

Contribution

It introduces new framizations for several knot algebras, expanding the theoretical framework and potential applications in knot theory.

Findings

Framization of Temperley--Lieb algebra achieved

Proposed framizations for BMW, B-type Hecke, and singular Hecke algebras

Motivated by Yokonuma--Hecke algebra structures

Abstract

This paper presents results on the framization of some knot algebras, defined by the authors. We explain the motivations of the concept of framization, coming from the Yokonuma--Hecke algebras, as well as recent results on the framization of the Temperley--Lieb algebra. Finally, we propose framizations for other knot algebras such as the BMW algebra, the $B$--type related Hecke algebras and the singular Hecke algebra.