Classification of Minimal Algebras over any Field up to Dimension 6
Algebraic Topology
2010-09-21 v2
Abstract
We give a classification of minimal algebras generated in degree 1, defined over any field of characteristic different from 2, up to dimension 6. This recovers the classification of nilpotent Lie algebras over up to dimension 6. In the case of a field of characteristic zero, we obtain the classification of nilmanifolds of dimension less than or equal to 6, up to -homotopy type. Finally, we determine which rational homotopy types of such nilmanifolds carry a symplectic structure.
Keywords
Cite
@article{arxiv.1001.3860,
title = {Classification of Minimal Algebras over any Field up to Dimension 6},
author = {Giovanni Bazzoni and Vicente Muñoz},
journal= {arXiv preprint arXiv:1001.3860},
year = {2010}
}
Comments
19 pages. Fully revised version. To appear in Transactions of the AMS