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.
|Number of pages||13|
|Journal||Communications in Algebra|
|State||Published - 3 May 2016|
- Grunewald-O'Halloran conjecture
- Nilpotent Lie algebras
- Vergne's conjecture