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Degenerations of 7-dimensional nilpotent Lie algebras. (English) Zbl 1126.17011
Summary: We study the varieties of Lie algebra laws and their subvarieties of nilpotent Lie algebra laws. We classify all degenerations of (almost all) five-step and six-step nilpotent seven-dimensional complex Lie algebras. One of the main tools is the use of trivial and adjoint cohomology of these algebras. In addition, we give some new results on the varieties of complex Lie algebra laws in low dimension.

MSC:
17B30 Solvable, nilpotent (super)algebras
17B56 Cohomology of Lie (super)algebras
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