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Minimal algebras and 2-step nilpotent Lie algebras in dimension 7
Authors:Giovanni Bazzoni
Affiliation:1. ICMAT (Instituto de Ciencias Matemáticas) CSIC-UAM-UC3M-UCM, Consejo Superior de Investigaciones Científicas, C/ Nicolás Cabrera 13-15, Campus Cantoblanco, UAM, 28049, Madrid, Spain
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:
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