2018/03/31 by Diego Conti, Federico A. Rossi
Mathematics · #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Central series #Computer science #Dimension (graph theory) #Discrete mathematics #Equivalence (formal languages) #Homotopy and Cohomology in Algebraic Topology #Lie algebra #Lie conformal algebra #Mathematics #Nice #Nilpotent #Nilpotent group #Pure mathematics #math.DG #msc:17B30 #msc:22E25 #msc:53C30
paper · pdf · doi:10.1016/j.jalgebra.2019.01.020
published as Journal of Algebra, Volume 525, 2019, Pages 311-340, ISSN 0021-8693 · 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
openalex publication_date 2019/02/05 · arxiv created 2019/02/15 · arxiv updated 2019/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.