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Models for solvable symplectic Lie groups. (English) Zbl 0846.58023

Summary: This paper investigates those Lie groups which admit left invariant symplectic structures. The present work deals with connected and simply connected completely real solvable Lie groups. This paper intends to give a complete solution to the existence problem above, which concerns the groupoid whose unit classes are simply connected solvable Lie groups. The first step consists in showing that left invariant symplectic geometry in solvable Lie groups is a by-product of the Koszul-Vinberg geometry in solvable Lie groups. The author proves a classification theorem by means of Koszul-Vinberg structures in solvable Lie groups.

MSC:

37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
22E25 Nilpotent and solvable Lie groups
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