Modular covariants of cyclic groups of order p

Article


Elmer, J. 2022. Modular covariants of cyclic groups of order p. Journal of Algebra. 598, pp. 134-155. https://doi.org/10.1016/j.jalgebra.2022.01.015
TypeArticle
TitleModular covariants of cyclic groups of order p
AuthorsElmer, J.
Abstract

Let G be a cyclic group of order p and let V, W be kG-modules. We study the modules of covariants k[V,W]^G = (S(V^∗) ⊗ W)^G . Recall that G has exactly p inequivalent indecomposable kG-modules, denoted V_n (n = 1, . . . , p) and V_n has dimension n. For any n, we show that k[V_2,V_n]^G is a free k[V_2]^G- module (recovering a result of Broer and Chuai) and we give an explicit set of covariants generating k[V_2,V_n]^G freely over k[V_2]^G . For any n, we show that k[V_3,V_n]^G is a Cohen-Macaulay k[V_3]^G -module (again recovering a result of Broer and Chuai) and we give an explicit set of covariants which generate k[V 3 , V n ] G freely over a homogeneous system of parameters for k[V_3]^G . We also use our results to compute a minimal generating set for the transfer ideal of k[V_3]^G over a homogeneous system of parameters.

KeywordsModular invariant theory; Covariants; Free module; Cohen-Macaulay; Hilbert series
LanguageEnglish
PublisherElsevier
JournalJournal of Algebra
ISSN0021-8693
Electronic1090-266X
Publication dates
Online03 Feb 2022
Print15 May 2022
Publication process dates
Deposited03 Feb 2022
Submitted14 Nov 2019
Accepted29 Jan 2022
Output statusPublished
Publisher's version
License
File Access Level
Open
Accepted author manuscript
License
File Access Level
Restricted
Copyright Statement

© 2022 The Author. Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Digital Object Identifier (DOI)https://doi.org/10.1016/j.jalgebra.2022.01.015
Web of Science identifierWOS:000793251800008
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