4 papers · 1 filter
Nilpotent Lie algebras of vector fields in three variables
Hassan Azad, Indranil Biswas, Ryad Ghanam
We give a complete constructive description of all finite dimensional nilpotent Lie algebras of smooth vector fields in three variables, including intransitive algebras. The descri…
Lie's classification of finite dimensional algebras of Vector Fields in C^N
Hassan Azad, Indranil Biswas, Said Waqas Shah
Brief proofs of classical results of Lie on finite dimensional subalgebras of vector fields in two and three variables are outlined. The results for algebras of maximal rank for ve…
On Lie's classification of nonsolvable subalgebras of vector fields on the plane
Hassan Azad, Indranil Biswas, Ahsan Fazil +1
A brief proof of Lie's classification of finite dimensional subalgebras of vector fields on the complex plane that have a proper Levi decomposition is given. The proof uses basic r…
Semisimple algebras of vector fields on C^N of maximal rank
Hassan Azad, Indranil Biswas, Fazal M. Mahomed
A classification of semisimple algebras of vector fields on C^N that have a Cartan subalgebra of dimension N is given. The proof uses basic representation theory and the local cano…