A dilemma of nonequivalent definitions of differential operators in noncommutative geometry

2007/02/27 by G. Sardanashvily, Sardanashvily, G.
Mathematics · Physics and Astronomy · #58J42 #81T75 #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #hep-th #math-ph #math.MP #math.QA #msc:58J42 #msc:81T75

paper · pdf · doi:10.48550/arxiv.math/0702850

17 pages

arxiv created 2007/02/27 · arxiv updated 2009/12/01

Abstract

In contrast with differential operators on modules over commutative and graded commutative rings, there is no satisfactory notion of a differential operator in noncommutative geometry.

Related

• On the notion of a differential operator in noncommutative geometry
• On the definition of higher order differential operators in noncommutative geometry
• Lectures on Differential Geometry of Modules and Rings
• Jets of modules in noncommutative geometry
• Lectures on graded differential algebras and noncommutative geometry