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On de Rham and Dolbeault cohomology of solvmanifolds. (English) Zbl 1352.22007
For a simply connected non-nilpotent solvable Lie group $$G$$ with a lattice $$\Gamma$$, the de Rham and Dolbeault cohomologies of $$G/\Gamma$$ are not in general isomorphic to the cohomologies of its Lie algebra $$\mathfrak g$$. This article constructs, up to a finite group, a new Lie algebra $$\widetilde{\mathfrak g}$$ whose cohomology is isomorphic to the de Rham cohomology of $$G/\Gamma$$. It also gives a Dolbeault version of such technique when $$G/\Gamma$$ is complex.

##### MSC:
 22E25 Nilpotent and solvable Lie groups 14F40 de Rham cohomology and algebraic geometry
##### Keywords:
solvmanifolds; de Rham cohomology; Dolbeault cohomology
Full Text:
##### References:
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