On semi-simplicity of KMY algebras

TL;DR

This paper investigates the structure of KMY algebras, demonstrating they are iterated inflation algebras, providing generators, and establishing conditions for their semisimplicity over complex numbers.

Contribution

It introduces a generator set for KMY algebras and proves their semisimplicity over complex fields when certain parameters are non-real.

Findings

KMY algebras are iterated inflation algebras

Generators for $J_{l,n}( ext{delta})$ are provided

Semisimplicity holds over complex numbers when $ ext{delta}$ is non-real

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.