The universal central extension of the holomorphic current algebra

Neeb KH, Wagemann F (2003)

Publication Type: Journal article, Original article

Publication year: 2003

Journal

Manuscripta Mathematica Springer Verlag (Germany)

Publisher: Springer Verlag (Germany)

Book Volume: 112

Pages Range: 441-458

Journal Issue: 4

DOI: 10.1007/s00229-003-0409-x

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.

Authors with CRIS profile

Karl Hermann Neeb Lehrstuhl für Mathematik (Lie-Gruppen und Darstellungstheorie)

How to cite

APA:

Neeb, K.H., & Wagemann, F. (2003). The universal central extension of the holomorphic current algebra. Manuscripta Mathematica, 112(4), 441-458. https://dx.doi.org/10.1007/s00229-003-0409-x

MLA:

Neeb, Karl Hermann, and Friedrich Wagemann. "The universal central extension of the holomorphic current algebra." Manuscripta Mathematica 112.4 (2003): 441-458.

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