English

Construction of nice nilpotent Lie groups

Differential Geometry 2019-02-18 v3

Abstract

We illustrate an algorithm to classify nice nilpotent Lie algebras of dimension nn up to a suitable notion of equivalence; applying the algorithm, we obtain complete listings for n9n\leq9. On every nilpotent Lie algebra of dimension 7\leq 7, we determine the number of inequivalent nice bases, which can be 00, 11, or 22. We show that any nilpotent Lie algebra of dimension nn has at most countably many inequivalent nice bases.

Keywords

Cite

@article{arxiv.1803.09248,
  title  = {Construction of nice nilpotent Lie groups},
  author = {Diego Conti and Federico A. Rossi},
  journal= {arXiv preprint arXiv:1803.09248},
  year   = {2019}
}

Comments

v3: 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

R2 v1 2026-06-23T01:04:16.570Z