Convergence of the Gutt Star Product
Journal of Lie theory, Tome 27 (2017) no. 2, pp. 579-622
We consider the Gutt star product viewed as an associative deformation of the symmetric algebra SA(g) over a Lie algebra g and discuss its continuity properties: we establish a locally convex topology on SA(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.
Classification :
53D55, 46H05, 46A03, 16S30
Mots-clés : Gutt star product, convergence, locally convex algebras, universal enveloping algebra
Mots-clés : Gutt star product, convergence, locally convex algebras, universal enveloping algebra
@article{JLT_2017_27_2_JLT_2017_27_2_a14,
author = {C. Esposito and P. Stapor and S. Waldmann},
title = {Convergence of the {Gutt} {Star} {Product}},
journal = {Journal of Lie theory},
pages = {579--622},
year = {2017},
volume = {27},
number = {2},
url = {http://geodesic.mathdoc.fr/item/JLT_2017_27_2_JLT_2017_27_2_a14/}
}
C. Esposito; P. Stapor; S. Waldmann. Convergence of the Gutt Star Product. Journal of Lie theory, Tome 27 (2017) no. 2, pp. 579-622. http://geodesic.mathdoc.fr/item/JLT_2017_27_2_JLT_2017_27_2_a14/