4 papers
Degenerations to filiform Lie algebras of dimension 9
Joan Felipe Herrera-Granada, Oscar Marquez, Sonia Vera
For most complex 9-dimensional filiform Lie algebra we find another non isomorphic Lie algebra that degenerates to it. Since this is already known for nilpotent Lie algebras of ran…
A distinguished example of filiform deformation
Joan Felipe Herrera-Granada, Paulo Tirao, Sonia Vera
We exhibit an example of a filiform (complex) Lie algebra of dimension 13 with all its ideals of codimension 1 being characteristically nilpotent, and we construct a non trivial fi…
Filiform Lie algebras of dimension 8 as degenerations
Joan Felipe Herrera-Granada, Paulo Tirao
For each complex 8-dimensional filiform Lie algebra we find another non isomorphic Lie algebra that degenerates to it. Since this is already known for nilpotent Lie algebras of ran…
The Grunewald-O'Halloran conjecture for nilpotent Lie algebras of rank >= 1
Joan Felipe Herrera-Granada, Paulo Tirao
Grunewald and O'Halloran conjectured in 1993 that every complex nilpotent Lie algebra is the degeneration of another, non isomorphic, Lie algebra. We prove the conjecture for the c…