A finite dimensional algebra of the diagram of a knot

TL;DR

This paper introduces a finite dimensional algebra linked to a knot diagram, providing a new algebraic perspective on knot projections with specific algebraic properties.

Contribution

It constructs a novel finite dimensional algebra from knot diagrams that is self-injective and special biserial, enriching the algebraic tools in knot theory.

Findings

Algebra is finite dimensional and non-commutative.

Algebra is self-injective and special biserial.

Provides a new algebraic invariant for knot projections.

Abstract

To a regular projection of a knot we associate a finite dimensional non-commutative associative algebra which is self-injective and special biserial.