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Esposito, C.* ; Stapor, P. ; Waldmann, S.*

Convergence of the gutt star product.

J. Lie Theory 27, 579-622 (2017)
DOI
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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Publikationstyp Artikel: Journalartikel
Dokumenttyp Wissenschaftlicher Artikel
Schlagwörter Convergence ; Gutt Star Product ; Locally Convex Algebras ; Universal Enveloping Algebra; Lie-algebra; Deformation; Quantization; Weyl
ISSN (print) / ISBN 0949-5932
e-ISSN 0940-2268
Zeitschrift Journal of Lie Theory
Quellenangaben Band: 27, Heft: 2, Seiten: 579-622 Artikelnummer: , Supplement: ,
Verlag Heldermann
Verlagsort Lemgo
Begutachtungsstatus Peer reviewed
Institut(e) Institute of Computational Biology (ICB)