On universal enveloping algebras in a topological setting

• Autorzy: Daniel Beltiţă , Mihai Nicolae
• Języki publikacji: EN

Abstrakty

EN

We study some embeddings of suitably topologized spaces of vector-valued smooth functions on topological groups, where smoothness is defined via differentiability along continuous one-parameter subgroups. As an application, we investigate the canonical correspondences between the universal enveloping algebra, the invariant local operators, and the convolution algebra of distributions supported at the unit element of any finite-dimensional Lie group, when one passes from finite-dimensional Lie groups to pre-Lie groups. The latter class includes for instance all locally compact groups, Banach-Lie groups, additive groups underlying locally convex vector spaces, and also mapping groups consisting of rapidly decreasing Lie group-valued functions.

Kategorie tematyczne

• 17B65: Infinite-dimensional Lie (super)algebras
• 22A10: Analysis on general topological groups
• 22E65: Infinite-dimensional Lie groups and their Lie algebras: general properties
• 22E66: Analysis on and representations of infinite-dimensional Lie groups

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2015
• Tom: 230
• Numer: 1
• Strony: 1-29

Daty

wydano

2015

Twórcy

autor

Daniel Beltiţă

• Institute of Mathematics "Simion Stoilow" of the Romanian Academy, P.O. Box 1-764, Bucureşti, Romania

autor

Mihai Nicolae

• Petroleum-Gas University of Ploieşti, Bd. Bucureşti no. 39, 100680 Ploieşti, Romania
• Institute of Mathematics "Simion Stoilow" of the Romanian Academy, P.O. Box 1-764, Bucureşti, Romania

Identyfikatory

DOI

10.4064/sm8003-12-2015