Identities of the Jones Monoid $\mathcal{J}_5$

TL;DR

This paper characterizes the identities satisfied by the Jones monoid _5, a mathematical structure relevant in knot theory, providing insights into its algebraic properties.

Contribution

It offers the first detailed characterization of the identities of the Jones monoid _5, advancing understanding of its algebraic structure.

Findings

Identifies the specific identities satisfied by _5

Provides a basis for the identities of _5

Enhances understanding of the algebraic properties of Jones monoids

Abstract

Jones monoids $\mathcal{J}_n$, for $1< n$, is a family of monoids relevant in knot theory. The purpose of this paper is to characterize of the identities satisfied by the Jones monoid $\mathcal{J}_5$.