About zero torsion linear maps on Lie algebras (Q555250)

Summary: We prove that any zero torsion linear map on a nonsolvable real Lie algebra \(\mathfrak g_0\) is an extension of some CR-structure. We then study the cases of \(\mathfrak {sl}(2, \mathbb R)\) and the 3-dimensional Heisenberg Lie algebra \(\mathfrak n\). In both cases, we compute up to equivalence all zero torsion linear maps on \(\mathfrak g_0\), and deduce an explicit description of the equivalence classes of integrable complex structures on \(\mathfrak g_0 \times \mathfrak g_0\).