Discriminants and Automorphism Groups of Veronese subrings of skew polynomial rings

TL;DR

This paper investigates the algebraic structure of Veronese subalgebras within q-skew polynomial rings, focusing on invariants like discriminants, centers, automorphism groups, and properties such as cancellation and the Tits alternative.

Contribution

It provides new insights into the invariants and automorphism groups of these subalgebras, advancing understanding of their algebraic and geometric properties.

Findings

Determined the discriminant and center of Veronese subalgebras.

Analyzed the automorphism groups of these subalgebras.

Established properties like cancellation and the Tits alternative for these rings.

Abstract

We study important invariants and properties of the Veronese subalgebras of $q$-skew polynomial rings, including their discriminant, center and automorphism group, as well as cancellation property and the Tits alternative.