Moscow-Petersburg seminar on low-dimensional mathematics
April 4, 2003, 16:00, room 311 of PDMI

M.M.Vinogradov (Moscow)
Algebraic differential calculus over modules and dioles.

One of the remarkable mathematical discoveries of the last century is finding
out the algebraic nature of differential calculus and developing a theory of
linear differential operators over arbitrary commutative algebras. We
present here a brief outline of this theory and formulate an algebraic
formalism describing the so-called Der-operators, that is, vector fields on
fiber bundles that cover vector fields on the base manifold. In order to do
this, a concept of diole is introduced, and differential calculus over diole
categories is built.

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http://www.pdmi.ras.ru/~lowdimma