An Atiyah Sequence for Noncommutative Principal Bundles

TL;DR

This paper develops a derivation-based Atiyah sequence framework for noncommutative principal bundles, addressing the conditions under which automorphisms of the quantum base lift to the total space, advancing noncommutative geometry theory.

Contribution

It introduces a derivation-based Atiyah sequence for noncommutative principal bundles and analyzes automorphism lifting conditions in quantum settings.

Findings

Established a derivation-based Atiyah sequence for noncommutative bundles

Identified criteria for lifting automorphisms from base to total space

Enhanced understanding of automorphism structures in quantum principal bundles

Abstract

We present a derivation-based Atiyah sequence for noncommutative principal bundles. Along the way we treat the problem of deciding when a given $^*$-automorphism on the quantum base space lifts to a $^*$-automorphism on the quantum total space that commutes with the underlying structure group.