Complex filiform Lie algebras of dimension 11

摘要

In this paper we give the explicit classification of complex filiform Lie algebras of dimension 11. To do this, we use a method previously obtained by us in an earlier paper, which is based on the concept of isomorphism between Lie algebras. At present, this explicit classification is not known, although Gómez, Jiménez and Khakimdjanov gave a list of these algebras in a non-explicit way, but in terms of cocycles. We find that there exist 188 families of complex filiform Lie algebras of dimension 11.