Lie Algebras : Classifications, Deformations, Rigidity and Differential Geometry

2008/05/05 by Goze, Michel
#17B05 #53C30 #53D05 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.0805.0468

Abstract

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.

Related

• Lie algebras : Classification, Deformations and Rigidity
• Rigidity of transformation groups in differential geometry
• Symplectic or contact structures on Lie Groups
• Deformation theory via differential graded Lie algebras
• Generalized Complex and Dirac Structures on Homogeneous Spaces