# Morita equivalences on Brauer algebras and BMW algebras of simply-laced types

## TL;DR

This paper investigates Morita equivalences for Brauer and BMW algebras of simply-laced types, revealing their structures as Morita equivalent to sums of group and Hecke algebras, respectively.

## Contribution

It establishes Morita equivalences for these algebras of simply-laced type, connecting them to group and Hecke algebras, especially for generic parameters.

## Key findings

- Brauer algebras are Morita equivalent to sums of group algebras of Coxeter groups.
- BMW algebras are Morita equivalent to sums of Hecke algebras of Coxeter groups.
- Results hold for algebras with generic parameters.

## Abstract

The Morita equivalences of classical Brauer algebras and classical Birman-Murakami-Wenzl algebras have been well studied. Here we study the Morita equivalence problems on these two kinds of algebras of simply-laced type, especially for them with the generic parameters. We show that Brauer algebras and Birman-Murakami-Wenzl algebras of simply-laced type are Morita equivalent to the direct sums of some group algebras of Coxeter groups and some Hecke algebras of some Coxeter groups, respectively.