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Derivations and non-commutative differential calculus. II. (Dérivations et calcul différentiel non commutatif. II.) (French. Abridged English version) Zbl 0829.16028
Let \(A\) be an associative algebra over \(\mathbb{R}\) or \(\mathbb{C}\) with a unit. In part I [M. Dubois-Violette, ibid. 307, 403-408 (1988; Zbl 0661.17012)] the notion of a graded differential algebra \(\Omega_{\text{Der}(A)}\) was introduced. One of the aims of this note is to show that, by introducing a new category of bimodules, the derivation \(d: A \to \Omega^1_{\text{Der} (A)}\) is characterized by a universal property.

16W25 Derivations, actions of Lie algebras
16W50 Graded rings and modules (associative rings and algebras)
17B56 Cohomology of Lie (super)algebras
16S32 Rings of differential operators (associative algebraic aspects)
58A12 de Rham theory in global analysis
46L85 Noncommutative topology
46L87 Noncommutative differential geometry
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