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Minimal algebras and $2-$step nilpotent Lie algebras in dimension 7 (1112.0109v1)
Published 1 Dec 2011 in math.AT and math.RA
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.