Displaying similar documents to “Globality in semisimple Lie groups”

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 ⊂ 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.