Deformations et rigidite geometrique des algebres de leibniz

A formal deformation of a Leibniz algebra A over a commutative ring k, consists of a formal series extending the Leibniz bracket of A, defined by fo We show that if f is a 2-cocycle for the cohomology of A with coefficients in its adjoint representation, a sufficient condition for the existence of F with f1=f, is the vanishing of the third cohomology group of A with coefficients in its adjoint representation. In the last section, we study deformations from the point of view of algebraic varieties.

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