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 this setting, this algebra becomes a polynomial identity (PI) algebra. It is known that simple modules over a PI algebra are finite dimensional with their dimension bounded above 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 characteristic.