# Truncations and extensions of the Brauer-Chen algebra

## TL;DR

This paper explores the representation theory of a generalized algebra related to complex reflection groups, introducing extensions and deformations that broaden understanding of algebraic structures in this domain.

## Contribution

It determines the generic representation theory of a key quotient of the Brauer-Chen algebra and introduces new algebra extensions with monodromic deformations.

## Key findings

- Representation theory of the algebra's quotient is characterized.
- Extensions of the algebra are defined and shown to admit deformations.
- The work generalizes classical algebraic structures to complex reflection groups.

## Abstract

The Brauer-Chen algebra is a generalization of the algebra of Brauer diagrams to arbitrary complex reflection groups, that admits a natural monodromic deformation. We determine the generic representation theory of the first non trivial quotient of this algebra. We also define natural extensions of this algebra and prove that they similarly admit natural monodromic deformations.