We illustrate an algorithm to classify nice nilpotent Lie algebras of dimension n up to a suitable notion of equivalence; applying the algorithm, we obtain complete listings for n≤9. On every nilpotent Lie algebra of dimension ≤7, we determine the number of inequivalent nice bases, which can be 0, 1, or 2. We show that any nilpotent Lie algebra of dimension n has at most countably many inequivalent nice bases.
Conti, D., Rossi, F. (2019). Construction of nice nilpotent Lie groups. JOURNAL OF ALGEBRA, 525, 311-340 [10.1016/j.jalgebra.2019.01.020].
Construction of nice nilpotent Lie groups
Conti, D;Rossi, FA
2019
Abstract
We illustrate an algorithm to classify nice nilpotent Lie algebras of dimension n up to a suitable notion of equivalence; applying the algorithm, we obtain complete listings for n≤9. On every nilpotent Lie algebra of dimension ≤7, we determine the number of inequivalent nice bases, which can be 0, 1, or 2. We show that any nilpotent Lie algebra of dimension n has at most countably many inequivalent nice bases.
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