1 - 10 of 11 articles
A short introduction to the theory of linear differential operators over commutative algebras is exposed.
The Poincaré δ-lemma (stable triviality of Spencer cohomology groups) for smooth algebras is proved.
Three definitions for characteristics of linear differential operators in the category of modules over a commutative unitary algebra are given. These definitions are compared with each other and some basic fact concerning their properties are proved. It is shown that for algebras without zero...
Let K ⊂ R ⊂ P be a tower of fields, N be a P-module, and Δ: R → N be a K-linear differential operator. The aim of this paper is to investigate whether the operator Δ has an extension to P, i.e. if these exists a differential operator Δ′: P → N such that Δ′|R = Δ. The results of this paper were...
The aim of this paper is to suggest an approach of constructing a residue theory. In particular, this approach may be used in case of infinite dimension of an algebra of differential forms. The results of the paper was announced without proofs in Uspekhi Mat. Nauk 35(2) (1980), 203–204.
This paper contains proofs and examples for some key facts about algebraic Spencer cohomologies preannounced elsewhere. The author hopes that here he has managed to build a more systematic discourse of the issues raised in earlier works.
A higher-order de Rham complex dR
σ  is associated with a commutative algebra A and a sequence of positive integers σ = (σ1σ2... It is called regular if σ is nondecreasing. We extend the algebraic definitions of the Lie derivative and interior product with respect to a derivation of A, to...
An axiomatic approach to the notion of adjoint operator is provided within the framework of the algebraic Lagrangian formalism.
The topic of this paper is the development of a differential calculus on a quantum space covariant with respect to the action of a quantum group. Quantized differential operators, jets, the de Rham and Spencer complexes, etc., are constructed. Also the integration over a quantum space, adjoint...
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