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We construct a universal continuous invariant bilinear form for the Liealgebra of compactly supported sections of a Lie algebra bundle in atopological sense. Moreover we construct a universal continuous centralextension of a current algebra that is the tensor product of afinite-dimensional Lie algebra g and a certain topological algebra A. Inparticular taking A as the compactly supported smooth functions on asigma-compact manifold M, we obtain a more detailed justification for a recentresult of Janssens and Wockel concerning a universal extension for the Liealgebra of compactly supported g-valued smooth functions on M.

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