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On some models in differential geometry. (Russian. English summary) Zbl 0813.46067

Summary: Some variants of axiomatics of algebras of “vector fields” in models of non-commutative differential geometry are considered. In the case of a commutative model (the De Rham complex) a matrix analogue of the Kadomtsev-Petviashvili hierarchy is constructed. The corresponding Sato system is presented. The method of deformations of \({\mathcal D}\)-modules is used.

MSC:

46L87 Noncommutative differential geometry
55R50 Stable classes of vector space bundles in algebraic topology and relations to \(K\)-theory
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