Invariant orders in Lie groups

Neeb, Karl-Hermann

Displaying similar documents to “Invariant orders in Lie groups”

Globality in semisimple Lie groups

Karl-Hermann Neeb (1990)

Annales de l'institut Fourier

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In the first section of this paper we give a characterization of those closed convex cones (wedges) $W$ in the Lie algebra $s l (2, R)^{n}$ which are invariant under the maximal compact subgroup of the adjoint group and which are controllable in the associated simply connected Lie group $S l (2, R)^{n^{\sim}}$ , i.e., for which the subsemigroup $S = (exp W)$ generated by the exponential image of $W$ agrees with the whole group $G$ (Theorem 13). In Section 2 we develop some algebraic tools concerning real root decompositions with respect to...

A note on Lie semialgebras in $𝔰𝔩 (2, ℝ)$ .

Breckner, Brigitte E. (2002)

Mathematica Pannonica

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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...