Minimal algebras and $2-$step nilpotent Lie algebras in dimension 7

Giovanni Bazzoni

Minimal algebras and $2-$step nilpotent Lie algebras in dimension 7

Algebraic Topology 2012-04-03 v1 Rings and Algebras

Authors: Giovanni Bazzoni

Abstract

We use the methods of \cite{BM} to give a classification of $7-$ dimensional minimal algebras, generated in degree 1, over any field $\bk$ of characteristic $\textrm{char}(\bk)\neq 2$ , whose characteristic filtration has length 2. Equivalently, we classify $2-$ step nilpotent Lie algebras in dimension 7. This classification also recovers the real homotopy type of $7-$ dimensional $2-$ step nilmanifolds.

Keywords

minimal algebras 2-step nilpotent Lie algebras nilmanifolds real homotopy type classification

Cite

@article{arxiv.1112.0109,
  title  = {Minimal algebras and $2-$step nilpotent Lie algebras in dimension 7},
  author = {Giovanni Bazzoni},
  journal= {arXiv preprint arXiv:1112.0109},
  year   = {2012}
}

Comments

18 pages, 1 figure

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