  In this paper we apply homotopical localization to the framework of
differential graded algebras over an operad. We get plus construction by
performing nullification with respect to an universal acyclic algebra. This
plus construction for Lie and Leibniz algebras up to homotopy yields two new
homology theories for associative algebras. They are closely related to cyclic
and Hochschild homologies. We also compute their first homology groups.
