Primitive ideals and representations
type: Item
instance of: scholarly article
title: Primitive ideals and representations
zbMATH Open document ID: 0598.17006
DOI: 10.1016/0021-8693(86)90208-5
author: Luis Casian
published in: Journal of Algebra
publication date: 1986-01-01T00:00:00Z
review text: Let \({\mathfrak g}\) be a semisimple Lie algebra over \({\mathbb{C}}\) and M a \({\mathfrak g}\)-module. Fix a primitive ideal I in the enveloping algebra U(\({\mathfrak J})\). The author studies the consequences in \({\mathfrak n}\)- cohomology of M of the condition \(IM=0\). Using a derived functor construction an analogue of the Casselman-Osborn theorem is proved in category \({\mathcal O}\) where the whole primitive ideal is fixed.
Mathematics Subject Classification ID: 17B56
Mathematics Subject Classification ID: 17B35
Mathematics Subject Classification ID: 17B55
Mathematics Subject Classification ID: 16D60
zbMATH DE Number: 3964120
zbMATH Keywords: semisimple Lie algebra
zbMATH Keywords: enveloping algebra
zbMATH Keywords: \({\mathfrak n}\)-cohomology
zbMATH Keywords: derived functor construction
zbMATH Keywords: category \({\mathcal O}\)
zbMATH Keywords: primitive ideal
reviewed by: Birgit Speh
MaRDI profile type: Publication
full work available at URL: 0021-8693(86)90208-5
OpenAlex ID: W2005339741
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description: scientific article; zbMATH DE number 3964120