Arens-Michael enveloping algebras and analytic smash products

Let g be a finite-dimensional complex Lie algebra, and let Û(g) be its universal enveloping algebra. We prove that if Û(g), the Arens-Michael envelope of U(g) is stably flat over U(g) (i.e., if the canonical homomorphism U (g) → Û(g) is a localization in the sense of Taylor (1972), then g is solvable. To this end, given a cocommutative Hopf algebra H and an H -module algebra A, we explicitly describe the Arens-Michael envelope of the smash product A#H as an "analytic smash product" of their completions w.r.t. certain families of seminorms. © 2006 American Mathematical Society.

Authors
Editors
-
Publisher
-
Number of issue
9
Language
English
Pages
2621-2631
Status
Published
Department
-
Number
-
Volume
134
Year
2006
Organizations
  • 1 Department of Nonlinear Analysis and Optimization, Faculty of Science, Peoples' Friendship University of Russia, Mikluho-Maklaya 6, 117198 Moscow, Russian Federation
Keywords
-
Date of creation
19.10.2018
Date of change
19.10.2018
Short link
https://repository.rudn.ru/en/records/article/record/3338/