Noncommutative Fibre Bundles via Bimodules
Operator Algebras
2024-12-31 v2 Quantum Algebra
Abstract
We construct a Leray-Serre spectral sequence for fibre bundles for de Rham sheaf cohomology on noncommutative algebras. The morphisms are bimodules with zero-curvature extendable bimodule connections. This generalises definitions involving differentiable algebra maps to differentiable completely positive maps by using the KSGNS construction and Hilbert -bimodules with bimodule connections. We give examples of noncommutative fibre bundles, involving group algebras, matrix algebras, and the quantum torus.
Cite
@article{arxiv.2302.00489,
title = {Noncommutative Fibre Bundles via Bimodules},
author = {Edwin J. Beggs and James E. Blake},
journal= {arXiv preprint arXiv:2302.00489},
year = {2024}
}