Centers and automorphisms of PI Quantum Matrix Algebras

Abstract

We study PI quantum matrix algebras and their automorphisms using the noncommutative discriminant. In the multi-parameter case at $n=2$ and $n=3$, we show that all automorphisms are graded when the center is a polynomial ring. In the single-parameter case, we determine a presentation of the center and show that the automorphism group is not graded, though are able to describe certain families of automorphisms in this case, as well as those of certain subalgebras.