A note on the exponential map and regular points in a reductive complex Lie group

Chu, Hsin

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Regular elements of semi-simple algebraic groups

Robert Steinberg (1965)

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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 $G = H S^{'}$ , $H \cap S = Z^{0}$ , where $H$ is a $H$ -group with...