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manuscripta mathematica

, Volume 112, Issue 4, pp 441–458 | Cite as

The universal central extension of the holomorphic current algebra

  • Karl-Hermann Neeb
  • Friedrich WagemannEmail author
Article

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⊂ℂ n . 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.

Keywords

Compact Subset Holomorphic Function Central Extension Current Algebra Differential Module 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  1. 1.Fachbereich MathematikTechnische Universität DarmstadtDarmstadtGermany
  2. 2.Laboratoire de Mathématiques Jean LerayFaculté des Sciences et Techniques, Université de NantesNantes cedex 3France

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