# Two Dimensional Representations of the Braid Group B3 and its Burau Representation Squared

## TL;DR

This paper classifies all two-dimensional irreducible complex representations of the braid group B3 and analyzes the decomposition of the squared Burau representation, providing insights into their structure.

## Contribution

It provides an elementary listing of all two-dimensional irreducible representations of B3 and decomposes the square of its Burau representation, a novel analysis in this context.

## Key findings

- Complete classification of 2D irreducible representations of B3
- Decomposition of the squared Burau representation
- Insights into the structure of B3 representations

## Abstract

We list the irreducible two dimensional complex representations of the Braid group B3 in elementary way. Then, we make a decomposition of the square of its irreducible Burau representation.