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On synthetic interpretation of quantum principal bundles

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arxiv 0912.0213 v1 pith:I2BQK3RT submitted 2009-12-01 math.QA

Tomasz Brzeziński This is my paper · ORCID
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keywords principalbundlescategorynoncommutativebundlequantumsyntheticalgebras
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Quantum principal bundles or principal comodule algebras are re-interpreted as principal bundles within a framework of Synthetic Noncommutative Differential Geometry. More specifically, the notion of a noncommutative principal bundle within a braided monoidal category is introduced and it is shown that a noncommutative principal bundle in the category opposite to the category of vector spaces is the same as a faithfully flat Hopf-Galois extension.

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  1. The reduced Dirac structure of General Relativity on manifolds with corners

    math-ph 2026-07 conditional novelty 7.0 of 10

    The reduced corner phase space of Palatini–Cartan gravity is a Dirac structure—the graph of a Poisson bivector—yielding a strict BF2V theory.

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