Traces of semi-invariants
Ela Celikbas, J\"urgen Herzog, Shinya Kumashiro
TL;DR
This paper develops a formula for computing traces of semi-invariants over rings of invariants related to finite groups, advancing understanding of their Gorenstein properties and local freeness.
Contribution
It introduces a new formula for traces of semi-invariants and explores its applications to Gorenstein and nearly Gorenstein conditions in invariant rings.
Findings
Provided a formula for traces of semi-invariants.
Derived criteria for Gorenstein and nearly Gorenstein properties.
Analyzed conditions for semi-invariants to be locally free.
Abstract
This article investigates the traces of certain modules over rings of invariants associated with finite groups. More precisely, we provide a formula for computing the traces of arbitrary semi-invariants, thereby contributing to the understanding of the non-Gorenstein locus of rings of invariants. Additionally, we discuss applications of this formula, including criteria for rings of invariants to be Gorenstein on the punctured spectrum and nearly Gorenstein, as well as criteria for semi-invariants to be locally free.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Commutative Algebra and Its Applications · Finite Group Theory Research