## 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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