  After recalling the construction of a graded Lie bracket on the space of
cyclic multilinear forms on a vector space V, due to Georges Pinczon and Rosane
Ushirobira, we prove this construction gives a structure of quadratic
associative algebra, up to homotopy, on V. In the associative case, it is easy
to refind the associated usual Hochshild cohomology. By considering restriction
to a subspace or a quotient space of forms, we can present in a completely
similar way the cases of quadratic commutative and quadratic Lie algebras, up
to homotopy, and the corresponding Harrison and Chevalley cohomologies.
