Jets of modules in noncommutative geometry

2003/10/23 by G. Sardanashvily, Sardanashvily, G.
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.math-ph/0310046

5 pages

arxiv created 2003/10/23 · openalex publication_date 2003/10/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Jets of modules over a commutative ring are well known to make up the representative objects of linear differential operators on these modules. In noncommutative geometry, jets of modules provide the representative objects only of a certain class of first order differential operators. As a consequence, a generalization of the standard Lagrangian formalism on smooth manifolds to noncommutative spaces is problematic.

Related

• On the notion of a differential operator in noncommutative geometry
• Jets and connections in commutative and noncommutative geometry
• Basics of jet modules and algebraic linear differential operators
• A dilemma of nonequivalent definitions of differential operators in noncommutative geometry
• Symbols in Noncommutative Geometry