  Given a symmetric non degenerated bilinear form b on a vector space V, G.
Pinczon and R. Ushirobira defined a bracket {,} on the space of multilinear
skewsymmetric forms on V. With this bracket, the quadratic Lie algebra
structure equation on (V, b) becomes simply {\^a, \^a} = 0. We characterize
similarly quadratic associative, commutative or pre-Lie structures on (V, b) by
the same equation {\^a, \^a} = 0, but on different spaces of forms. These
definitions extend to quadratic up to homotopy algebras and allows to describe
the corresponding cohomologies.
