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Twisted calculus. (English) Zbl 1414.16024

Summary: A twisted ring is a ring endowed with a family of endomorphisms satisfying certain relations. One may then consider the notions of twisted module and twisted differential module. We study them and show that, under some general hypothesis, the categories of twisted modules and integrable twisted differential modules are equivalent. As particular cases, one recovers classical results from the theory of finite difference equations or \(q\)-difference equations.

MSC:

16S32 Rings of differential operators (associative algebraic aspects)
05A30 \(q\)-calculus and related topics
13N10 Commutative rings of differential operators and their modules
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