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

The universal central extension of the holomorphic current algebra

  • Karl-Hermann Neeb
  • Friedrich WagemannEmail author


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.


Compact Subset Holomorphic Function Central Extension Current Algebra Differential Module 
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© 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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