The Grunewald–O'Halloran Conjecture for Nilpotent Lie Algebras of Rank ≥1

Joan Felipe Herrera-Granada, Paulo Tirao*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

Grunewald and O'Halloran conjectured in 1993 that every complex nilpotent Lie algebra is the degeneration of another, nonisomorphic, Lie algebra. We prove the conjecture for the class of nilpotent Lie algebras admitting a semisimple derivation, and also for 7-dimensional nilpotent Lie algebras. The conjecture remains open for characteristically nilpotent Lie algebras of dimension grater than or equal to 8.

Original languageEnglish
Pages (from-to)2180-2192
Number of pages13
JournalCommunications in Algebra
Volume44
Issue number5
DOIs
StatePublished - 3 May 2016
Externally publishedYes

Keywords

  • Deformations
  • Degenerations
  • Grunewald-O'Halloran conjecture
  • Nilpotent Lie algebras
  • Vergne's conjecture

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