A deformation of the \(*\)-product of Gutt on a reductive Lie algebra
type: Item
instance of: scholarly article
title: A deformation of the \(*\)-product of Gutt on a reductive Lie algebra
zbMATH Open document ID: 0792.58017
DOI: 10.1016/0393-0440(93)90035-D
published in: Journal of Geometry and Physics
publication date: 1993-12-10T00:00:00Z
review text: The author defines a family of star products on \(\mathbb{R}^ n\) which can be considered as deformation of the star product introduced by \textit{S. Gutt} in Lett. Math. Phys. 7, 249-258 (1983; Zbl 0522.58019) for the polynomial functions on \(\mathbb{R}^ n\). Here \(\mathbb{R}^ n\) is considered as abelian Lie algebra. A relation of the star product to the exponential of the Laplacian is given. The star product can be extended from the polynomial functions to the concentrated Gaussian on \(\mathbb{R}^ n\). Generalization to other Lie algebras are discussed.
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 17B99
Mathematics Subject Classification ID: 53D50
Mathematics Subject Classification ID: 32G07
zbMATH DE Number: 445208
zbMATH Keywords: star products
zbMATH Keywords: Lie algebras
author: Norman John Wildberger
reviewed by: M. Schlichenmaier
Wikidata QID: Q115363119
MaRDI profile type: Publication
cites work: Deformation theory and quantization. II: Physical applications
cites work: Q2548398
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cites work: Q5339349
cites work: An associative algebra of functions on the orbits of nilpotent Lie groups
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full work available at URL: 0393-0440(93)90035-d
OpenAlex ID: W1993953183
description: scientific article; zbMATH DE number 445208