Lie Algebras : Classifications, Deformations, Rigidity and Differential Geometry

Details Lie Algebras : Classifications, Deformations, Rigidity and Differential Geometry Lie Algebras : Classifications, Deformations, Rigidity and Differential Geometry

2008-05-05

arxiv.org/abs/0805.0468v1

Mathematics

Rings and Algebras

In French

Scientific paper

This is a short presentation of some classical results on finite dimensional complex Lie algebras (classification of nilpotent Lie algebras, deformations and perturbations, contractions and rigidity). We present some applications to Differential Geometry considering some left invariant structures on Lie groups : contact and symplectic structures, Generalized complex structures on real Lie Group. We present also the notion of riemannian and pseudo-riemannian G-symmetric spaces.

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