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.
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Bazzoni, G. Minimal algebras and 2-step nilpotent Lie algebras in dimension 7. Geom Dedicata 165, 111–133 (2013). https://doi.org/10.1007/s10711-012-9744-y
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DOI: https://doi.org/10.1007/s10711-012-9744-y