Centers and automorphisms of PI Quantum Matrix Algebras

2022/07/25 by Jason Gaddis, Gaddis, Jason, Thomas J. Lamkin +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2207.11956

openalex publication_date 2022/07/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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• Automorphisms and derivations of a universal left-symmetric enveloping algebra

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