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


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