The Dixmier map for nilpotent super Lie algebras
type: Item
instance of: scholarly article
title: The Dixmier map for nilpotent super Lie algebras
zbMATH Open document ID: 1275.17024
author: Estanislao Herscovich
published in: Communications in Mathematical Physics
publication date: 2012-08-13T00:00:00Z
full work available at URL: https://arxiv.org/abs/1009.1124
review text: The author extends the classical Dixmier map for nilpotent Lie algebras, to the setting of nilpotent super Lie algebras. In particular, using the existence of polarizations also in this case, he proves that if \(\mathfrak{g}=\mathfrak{g}_0\oplus\mathfrak{g}_1\) is a nilpotent super Lie algebra and \(\mathrm{Ad}_0\) is the adjoint group of \(\mathfrak{g}_0\), then there exists a bijective map \(I:\mathfrak{g}^\ast_0/\mathrm{Ad}_0\longrightarrow\mathrm{Prim}(U(\mathfrak{g}))\) sending an equivalence class \([\lambda]\) to a primitive ideal \(I(\lambda)\) of \(U(\mathfrak{g})\). This map coincides with the ordinary Dixmier map.
reviewed by: Panagiotis Batakidis
Mathematics Subject Classification ID: 17B30
Mathematics Subject Classification ID: 17B08
Mathematics Subject Classification ID: 17B35
zbMATH DE Number: 6065243
MaRDI profile type: Publication
OpenAlex ID: W2025599258
arXiv ID: 1009.1124
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DOI: 10.1007/S00220-012-1505-0
description: scientific article; zbMATH DE number 6065243