On jets, extensions and characteristic classes I

TL;DR

This paper develops a framework for non-commutative jets using square zero extensions and derivations, connecting affine jets to module liftings and relating the Kodaira-Spencer and Atiyah classes.

Contribution

It introduces general definitions of non-commutative jets and explores their relation to module liftings and characteristic classes.

Findings

Defined non-commutative jets using extensions and derivations

Connected affine jets to module liftings

Related Kodaira-Spencer class to Atiyah class

Abstract

In this paper we give general definitions of non-commutative jets in the local and global situation using square zero extensions and derivations. We study the functors Exank(A, I) where A is any k-algebra and I is any left and right A-module and use this to relate affine non-commutative jets to liftings of modules. We also study the Kodaira-Spencer class KS(L) and relate it to the Atiyah class.