Krohn--Rhodes complexity of Brauer type semigroups

TL;DR

This paper computes the Krohn--Rhodes complexity for the Brauer and annular semigroups, advancing understanding of their algebraic structure.

Contribution

It provides the first explicit calculation of Krohn--Rhodes complexity for these specific semigroups.

Findings

Krohn--Rhodes complexity of $rak{B}_n$ determined

Krohn--Rhodes complexity of $rak{A}_n$ determined

Results contribute to algebraic theory of semigroups

Abstract

The Krohn--Rhodes complexity of the Brauer semigroup $\mathfrak{B}_n$ and of the annular semigroup $\mathfrak{A}_n$ is computed.