Year: 2011
Type: preprint
Abstract: 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 $R_{\nabla_B}$ of a connection $\nabla_B$ 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.
Source: arXiv (Cornell University)
Author: Maakestad, Helge Øystein
Language: English
Topic: Advanced Topics in Algebra
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4298206729