A note on the simple modules over McConnell--Pettit algebras

TL;DR

This paper investigates simple modules over McConnell--Pettit algebras, demonstrating that induction and contraction processes produce simple modules at the bounds of the algebras' global dimension.

Contribution

It reveals how induction and contraction methods generate simple modules at the extremities of the global dimension for McConnell--Pettit algebras.

Findings

Induction yields simple modules at the lower end of global dimension.

Contraction yields simple modules at the upper end of global dimension.

Provides insight into the structure of simple modules over these algebras.

Abstract

We consider simple modules over the McConnell--Pettit algebras. We show that both induction and contraction yield simple modules for the extremes of the global dimension.