Geometriae Dedicata

, Volume 165, Issue 1, pp 111–133 | Cite as

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

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Abstract

We use the methods of Bazzoni and Muñoz (Trans Am Math Soc 364:1007–1028, 2012) to give a classification of 7-dimensional minimal algebras, generated in degree 1, over any field \({\mathbf{k}}\) of characteristic \({{\rm char}(\mathbf{k})\neq 2}\) , 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

Nilmanifolds Rational homotopy Nilpotent Lie algebras Minimal model 

Mathematics Subject Classification

Primary: 55P62 17B30 Secondary: 22E25 11E04 
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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.ICMAT (Instituto de Ciencias Matemáticas) CSIC-UAM-UC3M-UCM, Consejo Superior de Investigaciones CientíficasMadridSpain

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