Displaying similar documents to “Lie groups with smooth characters and with smooth semicharacters”

Classification of connected unimodular Lie groups with discrete series

Anh Nguyen Huu (1980)

Annales de l'institut Fourier

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We introduce a new class of connected solvable Lie groups called H -group. Namely a H -group is a connected solvable Lie group with center Z such that for some ℓ in the Lie algebra h of H , the symplectic for B ℓ on h / z given by ℓ ( [ 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...