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Convergence of the gutt star product.
J. Lie Theory 27, 579-622 (2017)
In this work we consider the Gutt star product viewed as an associative deformation of the symmetric algebra S•(g) over a Lie algebra g and discuss its continuity properties: we establish a locally convex topology on S• (g) such that the Gutt star product becomes continuous. Here we have to assume a mild technical condition on g: it has to be an Asymptotic Estimate Lie algebra. This condition is e.g. fulfilled automatically for all finite-dimensional Lie algebras. The resulting completion of the symmetric algebra can be described explicitly and yields not only a locally convex algebra but also the Hopf algebra structure maps inherited from the universal enveloping algebra are continuous. We show that all Hopf algebra structure maps depend analytically on the deformation parameter. The construction enjoys good functorial properties.
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Publication type
Article: Journal article
Document type
Scientific Article
Keywords
Convergence ; Gutt Star Product ; Locally Convex Algebras ; Universal Enveloping Algebra; Lie-algebra; Deformation; Quantization; Weyl
ISSN (print) / ISBN
0949-5932
e-ISSN
0940-2268
Journal
Journal of Lie Theory
Quellenangaben
Volume: 27,
Issue: 2,
Pages: 579-622
Publisher
Heldermann
Publishing Place
Lemgo
Reviewing status
Peer reviewed
Institute(s)
Institute of Computational Biology (ICB)