On semi-simplicity of KMY algebras

Abstract

We study the algebras, $J_{l,n}(\delta )$, introduced by Kadar-Martin-Yu in arXiv:1401.1774. We show that these algebras are iterated inflation algebras. We give a set of generators for $J_{l,n}(\delta )$. We show that this algebra satisifies the CMPX axiomatic framework in arXiv:math/0411395 when the base field is the complex numbers and $\delta \ne 0$. We show that $J_{l,n}(\delta )$ is semisimple over the complex numbers if $\delta$ is complex and not real.

21 pages