Harmonic functions on loop groups
Leonard Gross (1997-1998)
Séminaire Bourbaki
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Leonard Gross (1997-1998)
Séminaire Bourbaki
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Sergio Albeverio, Raphael Høegh-Krohn (1978)
Compositio Mathematica
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Christoph Wockel, Chenchang Zhu (2016)
Journal of the European Mathematical Society
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The purpose of this paper is to show how central extensions of (possibly infinite-dimensional) Lie algebras integrate to central extensions of étale Lie 2-groups in the sense of [Get09, Hen08]. In finite dimensions, central extensions of Lie algebras integrate to central extensions of Lie groups, a fact which is due to the vanishing of for each finite-dimensional Lie group. This fact was used by Cartan (in a slightly other guise) to construct the simply connected Lie group associated...
Neeb, Karl-Hermann (1996)
Journal of Lie Theory
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Teichmann, Josef (2001)
Journal of Lie Theory
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Hernández, I., Peniche, R. (2008)
International Journal of Mathematics and Mathematical Sciences
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Karl-Hermann Neeb (2002)
Annales de l’institut Fourier
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The main result of the present paper is an exact sequence which describes the group of central extensions of a connected infinite-dimensional Lie group by an abelian group whose identity component is a quotient of a vector space by a discrete subgroup. A major point of this result is that it is not restricted to smoothly paracompact groups and hence applies in particular to all Banach- and Fréchet-Lie groups. The exact sequence encodes in particular precise obstructions for a given...
G. Vranceanu (1964)
Annales Polonici Mathematici
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Baguis, P., Stavracou, T. (2002)
International Journal of Mathematics and Mathematical Sciences
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Paolo Baldi, Maurizia Rossi (2013)
Colloquium Mathematicae
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We investigate positive definiteness of the Brownian kernel K(x,y) = 1/2(d(x,x₀) + d(y,x₀) - d(x,y)) on a compact group G and in particular for G = SO(n).
Vaisman, Izu (2000)
Journal of Lie Theory
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Kriegl, Andreas, Michor, Peter W. (1997)
Journal of Lie Theory
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Kenny De Commer (2015)
Banach Center Publications
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On the level of Lie algebras, the contraction procedure is a method to create a new Lie algebra from a given Lie algebra by rescaling generators and letting the scaling parameter tend to zero. One of the most well-known examples is the contraction from 𝔰𝔲(2) to 𝔢(2), the Lie algebra of upper-triangular matrices with zero trace and purely imaginary diagonal. In this paper, we will consider an extension of this contraction by taking also into consideration the natural bialgebra structures...