Construction of nice nilpotent Lie groups

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 $n\le 9$. On every nilpotent Lie algebra of dimension $\le 7$, 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.

arXiv commentv3: Condition (N3) has been changed to exclude diagrams with arrows with the same label as the starting node, this will not affect the rest of the paper or the results, since this condition was implicitly assumed through the paper. Added a final remark 3.9. Presentation improved and bibliography updated. Article 28 Pages; Tables in ancillary file 137 pages

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Cited by in corpus (10)

• Ricci-flat and Einstein pseudoriemannian nilmanifolds
• Indefinite Einstein metrics on nice Lie groups
• Diagram involutions and homogeneous Ricci-flat metrics
• Symmetric and skew-symmetric complex structures
• The Ricci-flatness that lurks in weight
• Uniqueness of ad-invariant metrics
• Indefinite nilsolitons and Einstein solvmanifolds
• A construction of Einstein solvmanifolds not based on nilsolitons
• Nice pseudo-Riemannian nilsolitons
• Ad-invariant metrics on nonnice nilpotent Lie algebras