Universal continuous bilinear forms for compactly supported sections of Lie algebra bundles and universal continuous extensions of certain current algebras

2014/01/31 by Jan Milan Eyni, Eyni, Jan Milan
Mathematics · #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.RA #math.RT

paper · pdf · doi:10.48550/arxiv.1401.8154

21 pages

arxiv created 2014/01/31 · arxiv updated 2014/02/03

Abstract

We construct a universal continuous invariant bilinear form for the Lie algebra of compactly supported sections of a Lie algebra bundle in a topological sense. Moreover we construct a universal continuous central extension of a current algebra that is the tensor product of a finite-dimensional Lie algebra g and a certain topological algebra A. In particular taking A as the compactly supported smooth functions on a sigma-compact manifold M, we obtain a more detailed justification for a recent result of Janssens and Wockel concerning a universal extension for the Lie algebra of compactly supported g-valued smooth functions on M.

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