Globality in semisimple Lie groups

Karl-Hermann Neeb

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Invariant orders in Lie groups

Neeb, Karl-Hermann

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[For the entire collection see Zbl 0742.00067.]The author formulates several theorems about invariant orders in Lie groups (without proofs). The main theorem: a simply connected Lie group $G$ admits a continuous invariant order if and only if its Lie algebra $L (G)$ contains a pointed invariant cone. V. M. Gichev has proved this theorem for solvable simply connected Lie groups (1989). If $G$ is solvable and simply connected then all pointed invariant cones $W$ in $L (G)$ are global in $G$ (a Lie wedge $W \subset L (G)$ ...

On the definition of the dual Lie coalgebra of a Lie algebra.

Bertin Diarra (1995)

Publicacions Matemàtiques

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Let L be a Lie algebra over a field K. The dual Lie coalgebra Lº of L has been defined by W. Michaelis to be the sum of all good subspaces V of the dual space L* of L: V is good if m(V) ⊂ V ⊗ V, where m is the multiplication of L. We show that Lº = m(L* ⊗ L*) as in the associative case.

On subsemigroups of semisimple Lie groups

R. El Assoudi, J. P. Gauthier, I. A. K. Kupka (1996)

Annales de l'I.H.P. Analyse non linéaire

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Classification of endomorphisms of some Lie algebroids up to homotopy and the fundamental group of a Lie algebroid

Balcerzak, Bogdan

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