About Zero Torsion Linear Maps on Lie Algebras

Abstract EN

We prove that any zero torsion linear map on a nonsolvable real Lie algebra g0 is an extension of some CR-structure.

We then study the cases of sl(2, ℝ) and the 3-dimensional Heisenberg Lie algebra n.

In both cases, we compute up to equivalence all zero torsion linear maps on g0, and deduce an explicit description of the equivalence classes of integrable complex structures on g0×g0.