A note on central extensions of Lie groups.

Neeb, Karl-Hermann

Displaying similar documents to “A note on central extensions of Lie groups.”

Integrating central extensions of Lie algebras via Lie 2-groups

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 $π_{2}$ 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...

Heisenberg Lie bialgebras as central extensions.

Benayed, Miloud, Souidi, El Mamoun (1998)

The New York Journal of Mathematics [electronic only]

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Nambu-Lie groups.

Vaisman, Izu (2000)

Journal of Lie Theory

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Matched pairs and extensions of Lie bialgebras.

Miloud Benayed (1998)

Extracta Mathematicae

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Poisson-Lie groupoids and the contraction procedure

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...