Some rings of invariants that are Gorenstein

Tamir Buqaie – GJM, Volume 8, Issue 1 (2023), 78-82.

Post by: administration
octobre 26, 2023
Comments off

Let $G$ be a finite subgroup of $SL(V)$ and let $V$ be a $3$ -dimensional vector space over a finite field $\mathbb F$ of positive characteristic $p$ which divides $|G|.$ We denote by $S(V)$ the symmetric algebra and by $S(V)^{G}$ the subring of $G$ -invariants. Let $T(G)$ be the transvections group. In this paper we classify the Gorenstein rings of the form $S(V)^{G}$ , where $V$ is a decomposable $G$ -module of the form $V=\mathbb F v\oplus W$ , with $\mathbb F$ v and $W$ being $G$ -submodules with $\dim_\mathbb F W=2$ . There are several cases for $T(G)$ and $W$ , and so for each of them, we provide a sufficient and necessary condition for $G$ as above to ensure the Gorenstein property of $S(V)^G.$

Categories: Issue1

Milestones:

Received: September 22, 2022
Accepted: August 1, 2023
Revised: September 16, 2023
Published online: October 22, 2023

Authors:

Tamir Buqaie
Department of Mathematics,
Faculty of Natural Sciences, University of Haifa,
Mount Carmel, Haifa 31905, Israel.

Download:

Print Version