Brauer algebras of type H3 and H4

TL;DR

This paper introduces Brauer algebras linked to Coxeter groups of types H3 and H4, exploring their structure and properties, and relating them to known algebras D6 and E8 through admissible partitions.

Contribution

It constructs and analyzes Brauer algebras for types H3 and H4, extending the understanding of their algebraic properties and connections to existing algebraic frameworks.

Findings

Defined Brauer algebras for H3 and H4 types

Established their relation to D6 and E8 algebras

Described basic algebraic properties

Abstract

In this paper, we will present Brauer algebras associated to spherical Coxeter groups of type H3 and H4, which are also can be regarded as subalgebras of Brauer algebras D6 and E8 by Muhlherr's admissible partition. Also some basic properties will be described here.