Lie algebras : Classification, Deformations and Rigidity

Details Lie algebras : Classification, Deformations and Rigidity Lie algebras : Classification, Deformations and Rigidity

2006-11-26

arxiv.org/abs/math/0611793v1

Mathematics

Rings and Algebras

43 pages. Lessons given during the {\it Cinqui\`eme Ecole de G\'eom\'etrie Diff\'erentielle et Syst\`emes Dynamiques}, ENSET O

Scientific paper

In the first section we recall some basic notions on Lie algebras. In a second time we study the algebraic variety of complex $n$-dimensional Lie algebras. We present different notions of deformations : Gerstenhaber deformations, pertubations, valued deformations and we use these tools to study some properties of this variety. Finaly we introduce the concept of rigidity and we present some results on the class of rigid Lie algebras.

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