Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 18 (2022), 015, 22 pages      arXiv:2107.04653      https://doi.org/10.3842/SIGMA.2022.015

An Atiyah Sequence for Noncommutative Principal Bundles

Kay Schwieger a and Stefan Wagner b
a) iteratec GmbH, Zettachring 6, 70567 Stuttgart, Germany
b) Blekinge Tekniska Högskola, SE-371 79 Karlskrona, Sweden

Received July 26, 2021, in final form February 21, 2022; Published online March 07, 2022

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.

Key words: Atiyah sequence; noncommutative principal bundle; freeness; factor system.

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