On some models in differential geometry

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 $D$-modules is used. Bibliography: 14 titles.