On universal enveloping algebras in a topological setting

Daniel Beltiţă, and Mihai Nicolae. "On universal enveloping algebras in a topological setting." Studia Mathematica 230.1 (2015): 1-29. <http://eudml.org/doc/285796>.

@article{DanielBeltiţă2015,
abstract = {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.},
author = {Daniel Beltiţă, Mihai Nicolae},
journal = {Studia Mathematica},
keywords = {topological group; smooth function; test function; distribution; differential operator; enveloping algebra; exponential law; convolution},
language = {eng},
number = {1},
pages = {1-29},
title = {On universal enveloping algebras in a topological setting},
url = {http://eudml.org/doc/285796},
volume = {230},
year = {2015},
}

TY - JOUR
AU - Daniel Beltiţă
AU - Mihai Nicolae
TI - On universal enveloping algebras in a topological setting
JO - Studia Mathematica
PY - 2015
VL - 230
IS - 1
SP - 1
EP - 29
AB - 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.
LA - eng
KW - topological group; smooth function; test function; distribution; differential operator; enveloping algebra; exponential law; convolution
UR - http://eudml.org/doc/285796
ER -