Semisimplicity criterion for 2-tonal partition algebras

Abstract

We determine the semisimplicity criterion for even partition algebras over the complex field. Specifically we prove that the even/2-tonal partition algebras $P_n^2(\hat{I}´)$ over $\mathbb{C}$ are semisimple for all $n$ if and only if parameter $\hat{I}´\notin {\mathbb{N}}_0$ .

33 pages, multiple figures