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arXiv · 2502.19702

Some Constructions on Quantum Principal Bundles

Gustavo Amilcar Saldaña Moncada
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Abstract

This paper works as an appendix of the paper titled Geometry of Associated Quantum Vector Bundles and the Quantum Gauge Group and for paper titled Yang-Mills-Connes Theory and Quantum Principal SU(N)-Bundles. Here, we are going to prove four statements in the theory of quantum principal bundles:: 1) The universal differential envelope $\ast$--calculus of a matrix (compact) Lie group, for the classical bicovariant $\ast$--First Order Differential Calculus, is the algebra of differential forms. 2) An example of a quantum principal bundle in which the space of base forms is not generated by the base space. 3) The group isomorphism between convolution-invertible maps and covariant left module isomorphisms at the level of differential calculus 4) The way the maps $\{T^V_k \}$ from Remark 3.1 look in differential geometry.

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BibTeXRIS

Gustavo Amilcar Saldaña Moncada. 2026-08-27. Some Constructions on Quantum Principal Bundles. https://arxiv.org/abs/2502.19702

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