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On universal enveloping algebras in a topological setting

Volume 230 / 2015

Daniel Beltiţă, Mihai Nicolae Studia Mathematica 230 (2015), 1-29 MSC: Primary 22A10; Secondary 22E65, 22E66, 17B65. DOI: 10.4064/sm8003-12-2015 Published online: 25 January 2016

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.

Authors

  • Daniel BeltiţăInstitute of Mathematics “Simion Stoilow”
    of the Romanian Academy
    P.O. Box 1-764
    Bucureşti, Romania
    e-mail
    e-mail
  • Mihai NicolaePetroleum-Gas University of Ploieşti
    Bd. Bucureşti no. 39
    100680 Ploieşti, Romania
    and
    Institute of Mathematics “Simion Stoilow”
    of the Romanian Academy
    P.O. Box 1-764
    Bucureşti, Romania
    e-mail

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