On Simple Modules over the Quantum Matrix algebra at roots of unity

Abstract

This article investigates the two-parameter quantum matrix algebra at roots of unity. In the roots of unity setting, this algebra becomes a Polynomial Identity (PI) algebra and it is known that simple modules over such algebra are finite-dimensional with dimension at most the PI degree. We determine the center, compute the PI degree, and classify simple modules for two-parameter quantum matrix algebra, up to isomorphism, over an algebraically closed field of arbitrary characteristics.