On ideals in group algebras: an uncertainty principle and the Schur product - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Forum Mathematicum Année : 2022

On ideals in group algebras: an uncertainty principle and the Schur product

Résumé

In this paper we investigate some properties of ideals in group algebras of finite groups over fields. First, we highlight an important link between their dimension, their minimal Hamming distance and the group order. This is a generalized version of an uncertainty principle shown in 1992 by Meshulam. Secondly, we introduce the notion of the Schur product of ideals in group algebras and investigate the module structure and the dimension of the Schur square. We give a structural result on ideals that coincide with their Schur square, and we provide conditions for an ideal to be such that its Schur square has the projective cover of the trivial module as a direct summand. This has particularly interesting consequences for group algebras of p-groups over fields of characteristic p.
Fichier principal
Vignette du fichier
2202.12621 (1).pdf (171.48 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03852312 , version 1 (14-11-2022)

Identifiants

Citer

Martino Borello, Wolfgang Willems, Giovanni Zini. On ideals in group algebras: an uncertainty principle and the Schur product. Forum Mathematicum, 2022, ⟨10.1515/forum-2022-0064⟩. ⟨hal-03852312⟩
121 Consultations
45 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More