## Dérivations et calcul différentiel non commutatif. (Derivations and non-commutative differential calculus).(French)Zbl 0661.17012

The canonical operation of the Lie algebra Der($${\mathcal A})$$ of derivations of an algebra $${\mathcal A}$$ with a unit in the graded differential algebra $$\Omega$$ ($${\mathcal A})$$ is studied. Different graded differential algebras associated with this operation are introduced. A filtration of $$\Omega$$ ($${\mathcal A})$$ associated with the operation of Der($${\mathcal A})$$ is defined and investigated. Some natural examples in which $${\mathcal A}=C^{\infty}(V)$$ (V-paracompact $$C^{\infty}$$-manifold) and $${\mathcal A}=M_ n({\mathbb{C}})$$ (the Lie algebra of endomorphisms of $${\mathbb{C}}^ n)$$ are considered.
Reviewer: J.Kubarski

### MSC:

 17B56 Cohomology of Lie (super)algebras 58A12 de Rham theory in global analysis 53C99 Global differential geometry