The generic representation theory of the Juyumaya algebra of braids and ties

TL;DR

This paper explores the representation theory of the Juyumaya algebra, revealing its connection to the small ramified partition algebra and providing a comprehensive understanding of its structure.

Contribution

It establishes an isomorphism between a specialization of the Juyumaya algebra and the small ramified partition algebra, advancing the algebra's theoretical framework.

Findings

Identification of the complex generic representation theory of the Juyumaya algebra

Demonstration of isomorphism with the small ramified partition algebra

Enhanced understanding of algebraic structures related to braids and ties

Abstract

In this paper we determine the complex generic representation theory of the Juyumaya algebra. We show that a certain specialization of this algebra is isomorphic to the small ramified partition algebra, introduced by P. Martin.