Algèbres graduées avec symétries

In this paper we define the notion of “graded algebra with symmetries”. This notion is a generalization of the extended differential forms. We prove that for a graded algebra with symmetries T, we associate a subalgebra Ω⁎ which generalizes the noncommutative differential forms. Using this algebra Ω⁎, we can define the Hochschild and cyclic homologies, cup i-products and the Steenrod squares.