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Classification of indefinite hyper-Kaehler symmetric spaces
Dmitri V. Alekseevsky, Vicente Cortes
We classify indefinite simply connected hyper-Kaehler symmetric spaces. Any such space without flat factor has commutative holonomy group and signature (4m,4m). We establish a natu…
Extensions of Lie algebras
Dmitri Alekseevsky, Peter W. Michor, Wolfgang Ruppert
We review (non-abelian) extensions of a given Lie algebra, identify a 3-dimensional cohomological obstruction to the existence of extensions. A striking analogy to the setting of c…
Lifting smooth curves over invariants for representations of compact Lie groups
Dmitri Alekseevsky, Andreas Kriegl, Mark Losik +1
We show that one can lift locally real analytic curves from the orbit space of a compact Lie group representation, and that one can lift smooth curves even globally, but under an a…