Nilmanifolds and associated Lie algebras over the integers

Bohumil Cenkl and Richard Porter

Vol. 193 (2000), No. 1, 5–29

DOI: 10.2140/pjm.2000.193.5

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.

Milestones

Received: 11 June 1998

Published: 1 March 2000