On the orbit method for the Lie algebra of vector fields on a curve
type: Item
instance of: scholarly article
title: On the orbit method for the Lie algebra of vector fields on a curve
zbMATH Open document ID: 0908.17008
author: Rosane Ushirobira
published in: Journal of Algebra
publication date: 1998-10-26T00:00:00Z
review text: Let \(G\) be the Lie algebra of vector fields on an affine smooth curve. With any element \(\lambda\in G^*\) having finite rank, one associates a canonical polarization \(P\). The main result of the paper presents a criterion for the induced module \(\text{Ind}_P^G(\lambda)\) to be simple. Moreover, it is proved that for any \(\lambda\) as above, the annihilator of \(\text{Ind}_P^G(\lambda)\) in \(U(G)\) is a primitive ideal. This theorem suggests the idea of a Dixmier map for \(G\). Finally, the author calculates the Gelfand-Kirillov dimension of \(\text{Ind}_P^G(\lambda)\) and conjectures that the annihilator of \(\text{Ind}_P^G(\lambda)\) in \(U(G)\) has finite Gelfand-Kirillov codimension.
reviewed by: Volodymyr Mazorchuk
Mathematics Subject Classification ID: 17B35
Mathematics Subject Classification ID: 17B66
Mathematics Subject Classification ID: 17B10
zbMATH DE Number: 1200014
zbMATH Keywords: orbit method
zbMATH Keywords: algebra of vector fields
zbMATH Keywords: induced representation
zbMATH Keywords: Dixmier map
zbMATH Keywords: primitive ideal
Wikidata QID: Q115395900
MaRDI profile type: Publication
OpenAlex ID: W2169723552
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DOI: 10.1006/JABR.1997.7338
description: scientific article; zbMATH DE number 1200014