Brauer algebras of type B

TL;DR

This paper introduces a new algebraic structure called the Brauer algebra of type B, defined via generators and relations, and explores its properties, including its relation to other Brauer algebras and its cellular structure.

Contribution

It defines the Brauer algebra of type B, shows its embedding into the Brauer algebra of type D, and identifies its cellular structure, extending the theory of Brauer algebras of classical types.

Findings

The algebra is a subalgebra of the Brauer algebra of type Dn+1.

It possesses a cellular structure.

It generalizes the concept of Brauer algebras of type Cn.

Abstract

For each n>0, we define an algebra having many properties that one might expect to hold for a Brauer algebra of type Bn. It is defined by means of a presentation by generators and relations. We show that this algebra is a subalgebra of the Brauer algebra of type Dn+1 and point out a cellular structure in it. This work is a natural sequel to the introduction of Brauer algebras of type Cn, which are subalgebras of classical Brauer algebras of type A2n-1 and differ from the current ones for n>2.