Twisted calculus
Bernard Le Stum (IRMAR), Adolfo Quir\'os
TL;DR
This paper explores the theory of twisted rings and modules, establishing an equivalence between categories of twisted modules and integrable twisted differential modules, generalizing classical difference and q-difference equations.
Contribution
It introduces a unifying framework for twisted modules and differential modules, extending classical difference equation theories under broad conditions.
Findings
Categories of twisted modules and integrable twisted differential modules are equivalent.
Recovers classical results from finite difference and q-difference equations.
Provides a general theoretical foundation for twisted algebraic structures.
Abstract
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.
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Taxonomy
TopicsPolynomial and algebraic computation · Algebraic structures and combinatorial models · Commutative Algebra and Its Applications