Table of Contents
ISRN Algebra
Volume 2011 (2011), Article ID 930189, 16 pages
http://dx.doi.org/10.5402/2011/930189
Research Article

About Zero Torsion Linear Maps on Lie Algebras

Institut de Mathématiques de Bourgogne, UMR CNRS 5584, Université de Bourgogne, BP 47870, 21078 Dijon Cedex, France

Received 6 May 2011; Accepted 31 May 2011

Academic Editors: A. De Sole, A. Isaev, A. V. Kelarev, and A. Kiliçman

Copyright © 2011 Louis Magnin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We prove that any zero torsion linear map on a nonsolvable real Lie algebra 𝔀 0 is an extension of some CR-structure. We then study the cases of 𝔰 𝔩 (2, ℝ ) and the 3-dimensional Heisenberg Lie algebra 𝔫 . In both cases, we compute up to equivalence all zero torsion linear maps on 𝔀 0 , and deduce an explicit description of the equivalence classes of integrable complex structures on 𝔀 0 Γ— 𝔀 0 .