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 $P_n^2(\delta)$ over $\mathbb{C}$ are semisimple for all $n$ if and only if parameter $\delta \not\in \mathbb{N}_0$ .