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The universal central extension of the holomorphic current algebra

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Abstract.

We identify the universal differential module Ω1(A) for the Fréchet algebra A of holomorphic functions on a complex Stein manifold X, and more generally on a Riemannian domain R over X and for the algebra of germs of holomorphic functions on a compact subset K⊂ℂn. It turns out to be isomorphic to the Fréchet space of holomorphic 1-forms on X, resp. R, resp. to the space Ω1(K) of germs of holomorphic 1-forms in K. This determines the center of the universal central extension of the Lie algebra 𝒪(R,𝔨 of holomorphic maps from R to a finite-dimensional simple complex Lie algebra 𝔨.

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Authors and Affiliations

  1. Fachbereich Mathematik, Technische Universität Darmstadt, Schlossgartenstr. 7, 64285, Darmstadt, Germany

    Karl-Hermann Neeb

  2. Laboratoire de Mathématiques Jean Leray, Faculté des Sciences et Techniques, Université de Nantes, 2, rue de la Houssinière, 44322, Nantes cedex 3, France

    Friedrich Wagemann

Authors
  1. Karl-Hermann Neeb
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  2. Friedrich Wagemann
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Correspondence to Friedrich Wagemann.

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Neeb, KH., Wagemann, F. The universal central extension of the holomorphic current algebra. manuscripta math. 112, 441–458 (2003). https://doi.org/10.1007/s00229-003-0409-x

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