LAUSR

Abstract Given a symmetric non-degenerate bilinear form b on a vector space g , G. Pinczon and R. Ushirobira have defined a bracket { , } on the space of multilinear skewsymmetric forms on g . With this bracket, the quadratic Lie algebra structure equation on ( g , b ) becomes simply { Ω , Ω } = 0 . Following the same program, we characterize the quadratic hom-right symmetric structures on ( g , b ) by the same equation { Ω , Ω } = 0 , on the space of ‘bi-symmetric’ forms. This characterization extends to quadratic hom-right symmetric algebras up to homotopy and allows us to describe the corresponding cohomology.