Geometric and Harmonic Analysis on Homogeneous Spaces and Applications by Ali Baklouti & Takaaki Nomura

Author:Ali Baklouti & Takaaki Nomura
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

In [4], a proof of Theorem 1.1 is provided when G is simply connected. Thus we shall only treat the non-simply connected case. In the case where is abelian, the property of stability fails to hold in general and depends upon the structure and the position of H and inside G (cf. [3] and [9]).

2 On Reduced Threadlike Lie Groups

2.1 A Glimpse on Threadlike Structures

From now on and unless a specific mention, we suppose that -span the associated Lie algebra of The subspace -span is clearly a one codimensional abelian ideal of The center of is however one dimensional and it is the space -span Let be the connected and simply connected Lie group associated to and the exponential map which is a global -diffeomorphism from into The reduced threadlike Lie group G is the quotient of by the central discrete subgroup The corresponding exponential map is given by:

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