Finite dimensional representations of \(\Gamma(\sigma_ 1,\sigma_ 2,\sigma_ 3)\)
type: Item
instance of: scholarly article
title: Finite dimensional representations of \(\Gamma(\sigma_ 1,\sigma_ 2,\sigma_ 3)\)
zbMATH Open document ID: 0827.17030
author: Yi Ming Zou
published in: Journal of Algebra
publication date: 1995-12-12T00:00:00Z
review text: The algebra considered here is the Lie superalgebra \(G= \Gamma (\sigma_1, \sigma_2, \sigma_3)\), which is denoted by \(D(2, 1; \alpha)\) in Kac's notation [\textit{V. G. Kac}, Adv. Math. 26, 8-96 (1977; Zbl 0366.17012)]. Using the technique of Bernstein, Gelfand and Gelfand the author gives a list of singly generated finite dimensional indecomposable representations for \(G\), and shows that any finite dimensional representation of \(G\) is a quotient of a direct sum of some representations from the list. Essentially, this list consists of the irreducible highest weight \(G\)-modules and of indecomposable \(G\)-modules of which the character is a sum of characters of irreducible so-called atypical modules.
Mathematics Subject Classification ID: 17B70
Mathematics Subject Classification ID: 17A70
Mathematics Subject Classification ID: 17B10
zbMATH DE Number: 701279
zbMATH Keywords: highest weight modules
zbMATH Keywords: indecomposable modules
zbMATH Keywords: Lie superalgebra
zbMATH Keywords: indecomposable representations
MaRDI profile type: Publication
full work available at URL: jabr.1994.1311
OpenAlex ID: W2078836314
DOI: 10.1006/JABR.1994.1311
description: scientific article; zbMATH DE number 701279