PreprintarXiv licencearXiv
Reduction of structure groups for noncommutative principal bundles
Abstract
Let G be a compact group and let H ⊆ G be a closed subgroup. We study reduction of the structure group for noncommutative principal bundles, modelled by free C*-dynamical systems in the sense of Ellwood. We first describe how induction from H to G behaves on associated correspondences and their tensor structure. Using reconstruction, this leads to a Tannakian characterization of reduction of the structure group in terms of the associated tensor functor. For normal subgroups, we characterize reduction in terms of central equivariant homomorphisms and derive module- and K-theoretic obstructions. We conclude with a noncommutative O(n)-example which admits no reduction to SO(n).
Related
- Intrinsic Non-Reductive Geometric Invariant Theory and Moduli Spaces of Principal Bundles with Non-Reductive Structure Groups
- Reduction of symmetric time-dependent Hamiltonian systems I: presymplectic principal ℝ-bundles
- Helly Numbers for Connected Reductive Groups and Splitting of Toric Principal Bundles
- On the Geometric Structure of Hyperbolic Clifford Bundles and Associated Spin Groups
- Generalized Killing spinors as Lagrangian sections of principal spin bundles
BibTeX
@misc{wagner2026reduction,
title = {{Reduction of structure groups for noncommutative principal bundles}},
author = {Stefan Wagner},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26590},
eprint = {2610.26590},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26590},
}
RIS
TY - UNPB
TI - Reduction of structure groups for noncommutative principal bundles
AU - Stefan Wagner
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.26590
UR - https://arxiv.org/abs/2610.26590
AB - Let G be a compact group and let H ⊆ G be a closed subgroup. We study reduction of the structure group for noncommutative principal bundles, modelled by free C^*-dynamical systems in the sense of Ellwood. We first describe how induction from H to G behaves on associated correspondences and their tensor structure. Using reconstruction, this leads to a Tannakian characterization of reduction of the structure group in terms of the associated tensor functor. For normal subgroups, we characterize reduction in terms of central equivariant homomorphisms and derive module- and K-theoretic obstructions. We conclude with a noncommutative O(n)-example which admits no reduction to SO(n).
ER -