We investigate algebras with one operation. We study when these algebras form a monoidal category and analyze Koszulness and cyclicity of the corresponding operads. We also introduce a new kind of symmetry for operads, the dihedrality, responsible for the existence of dihedral cohomology.The main trick, which we call the polarization, will be used to represent an algebra with one operation without any specific symmetry as an algebra with one commutative and one anticommutative operations. We will try to convince the reader that this change of perspective might sometimes lead to new insights and results.This point of view was used by Livernet and Loday to introduce a one-parameter family of operads whose specialization at 0 is the operad for Poisson algebras, while at a generic point it equals the operad for associative algebras. We study this family and explain how it can be used to interpret the deformation quantization ( * -product) in a neat and elegant way.

A Lie-admissible algebra gives a Lie algebra by anticommutativity. In this work we describe remarkable types of Lie-admissible algebras such as Vinberg algebras, pre-Lie algebras or Lie algebras. We compute the corresponding binary quadratic operads and study their duality. Considering Lie algebras as Lie-admissible algebras, we can define for each Lie algebra a cohomology with values in an Lie-admissible module. This leads to the study some deformations of Lie algebras in the classes of Lie-admissible algebras.

We present classes of nonassociative algebras whose associator satisfies invariance conditions given by the action of the 3 order symmetric group. Amongst these algebras we find the wellknown Vinberg algebras, the Pre-Lie algebras, the Lie-admissible algebras and the 3-power associative algebras. * Email address: M.Goze@uha.fr (Un)The following diagram is commutative : t t t t t t t tA

Poisson algebra is usually defined to be a commutative algebra together with a Lie bracket, and these operations are required to satisfy the Leibniz rule. We describe Poisson structures in terms of a single bilinear operation. This enables us to explore Poisson algebras in the realm of non-associative algebras. We study their algebraic and cohomological properties, their deformations as non-associative algebras, and settle the classification problem in low dimensions.