On the category of Harish-Chandra block modules
type: Item
instance of: scholarly article
title: On the category of Harish-Chandra block modules
author: Dylan Fillmore
published in: Journal of Algebra
publication date: 2024-09-03T00:00:00Z
review text: The author generalizes the following result of \textit{Yu. A. Drozd} et al. [NATO ASI Ser., Ser. C, Math. Phys. Sci. 424, 79--93 (1994; Zbl 0812.17007)] (dropping the assumption that \(G\) is quasicommutative): when \(G\) is a Harish-Chandra subalgebra of \(A\) the structure of Harish-Chandra \(A\)-modules can be described using information about the relationship between \(A\) and the cofinite maximal ideals of \(G\). The author introduces Harish-Chandra block modules and extend the previous result to these modules (Section 3.4).\N\NThe notion of strong Harish-Chandra block modules allows to clarify ambiguities in the work of Drozd, Futorny, and Ovsienko [loc. cit.], raised by the possibility of infinite- dimensional generalized weight spaces (Theorem 1.2).
reviewed by: Luz Adriana Mejia Castaño
Mathematics Subject Classification ID: 16D90
Mathematics Subject Classification ID: 17B10
zbMATH DE Number: 7905989
zbMATH Keywords: representation theory
zbMATH Keywords: Harish-Chandra modules
zbMATH Keywords: Harish-Chandra block modules
zbMATH Keywords: block modules
zbMATH Keywords: Harish-Chandra subalgebra
zbMATH Keywords: Harish-Chandra block subalgebra
MaRDI profile type: Publication
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DOI: 10.1016/J.JALGEBRA.2024.06.022
description: scientific article; zbMATH DE number 7905989