The notion of adapted complex structure is extended from Riemannian manifolds to general Koszul connections. The case of the canonical connection of a Lie group and the Levi-Civita connection of a pseudo-Riemannian manifold is studied.doi:10.1007/s00208-004-0525-2Róbert Szke...
Lie Group Structures on Quotient Groups and Universal Complexifications for Infinite-Dimensional Lie Groups We characterize the existence of Lie group structures on quotient groups and the existence of universal complexifications for the class of Baker-Campbell-H......
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If M is regular and the complexified modeling space of M is normal, then a regular complexification exists for some neighborhood of K. For each (real or complex) analytic regular manifold M modeled on a metrizable locally convex space and Banach-Lie group H, this allows the group Germ(K...
We show that X can be regarded as a G-invariant domain in a "universal" complex manifold X* on which the complexification$({\\mathbb C},+)$of G acts. The analogous result holds for actions of a larger class of real Lie groups containing, e.g. abelian and certain nilpotent ones. ...
We characterize the existence of Lie group structures on quotient groups and the existence of universal complexifications for the class of Baker-Campbell-Hausdorff (BCH-) Lie groups, which subsumes all Banach-Lie groups and "linear" direct limit Lie groups, as well as the mapping groups C Kr...
The complexification of K introduced by Donadson is not a group, only a "formal Lie group". However it still makes sense to talk about the exponential map in the complexification. In this note we show how to construct geometrically the exponential map (for small time), in case the ...
semisimple Lie groupsymmetric spacehomogeneous CR-structureLet G/K be a noncompact Riemannian symmetric space and let GC/KC be its complexification. Then G acts on GC/KC by left translations. We study the invariant CR-structure of the closed G-orbits of maximal dimension and determine which ...
We consider the action of a real semisimple Lie group G on the complexification G C / H C of a semisimple symmetric space G / H and we present a refinement of Matsukiʼs results (Matsuki, 1997 [1]) in this case. We exhibit a finite set of points in G C / H C , sitting on...
LiealgebraNon-HermitianHamiltoniansPTsymmetryrealeigenvaluesregulareigenfunctionsA new kind of PT and non-PT -symmetric complex potentials are constructed from a group theoretical viewpoint of the sl(2,C) potential algebras. The real eigenvalues and the corresponding regular eigenfunctions are also ...