Abstract

We consider the correspondence between nilmanifolds and Lie algebras with rational basis, and we define spectral sequences converging to the respective cohomologies. The E₂ terms of the spectral sequences are the cohomolgies of isomorphic graded Lie algebras.

Each nilmanifold gives rise to a Lie algebra with rational basis. We give an example which illustrates that not all such Lie algebras correspond to nilmanifolds. Given a Lie algebra with rational basis we give a construction that produces a nilmanifold with Lie algebra that is rationally equivalent to the starting Lie algebra.

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