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Classification of almost spherical pairs of compact simple Lie groups

Ihor Mykytyuk, Anatoly Stepin (2000)

Banach Center Publications

All homogeneous spaces G/K (G is a simple connected compact Lie group, K a connected closed subgroup) are enumerated for which arbitrary Hamiltonian flows on T*(G/K) with G-invariant Hamiltonians are integrable in the class of Noether integrals and G-invariant functions.

Classification of connected unimodular Lie groups with discrete series

Anh Nguyen Huu (1980)

Annales de l'institut Fourier

We introduce a new class of connected solvable Lie groups called H -group. Namely a H -group is a unimodular connected solvable Lie group with center Z such that for some in the Lie algebra h of H , the symplectic for B on h / z given by ( [ x , y ] ) is nondegenerate. Moreover, apart form some technical requirements, it will be proved that a connected unimodular Lie group G with center Z , such that the center of G / Rad G is finite, has discrete series if and only if G may be written as G = H S ' , H S = Z 0 , where H is a H -group with...

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