On matrix representations for generalized braid groups

TL;DR

This paper introduces new matrix representations for generalized braid groups, extending classical representations like Burau and Gassner through iterative procedures, enhancing understanding of their algebraic structures.

Contribution

It presents novel matrix representations for generalized braid groups, including an iterative method to extend the Gassner representation, broadening the scope of braid group representations.

Findings

New matrix representations for generalized braid groups

Iterative procedure for extending Gassner representation

Enhanced algebraic understanding of braid groups

Abstract

In the present paper, we construct a variant of the Burau representation of two generalizations of the classical braid group. For the Gassner representation, we propose an iterative procedure to find and generalize the extension of this representation.