2011/10/22 by Helge Øystein Maakestad, Maakestad, Helge Øystein
Mathematics · Physics and Astronomy · #14F10 #14F40 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.1110.4966
openalex publication_date 2011/10/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we give explicit formulas for higher order differential operators on a finitely generated projective module E on an arbitrary commutative unital ring A. We use the differential operators constructed to give a simple formula for the curvature of a classical connection and a connection on a Lie-Rinehart algebra in terms of a "projective basis" B for E. A "projective basis" is sometimes referred to as a "dual basis". This gives an explicit formula for the curvature R∇B of a connection ∇B on E defined in terms of a projective basis B and an idempotent ϕ for E. We also consider the notion of a stratification on the module E induced by a projective basis B. It turns out few stratifications are induced by a projective basis.