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<p>It is well–known that, given a principal <i>G</i>–bundle equipped with a principal connection, one can associate to every unitary finite–dimensional representation of <i>G</i> a linear connection and a compatible Hermitian structure on the corresponding associated vector bundle. Moreover, the gauge group acts both on the space of principal connections and on the space of induced linear connections defined on the associated vector bundles. The aim of this paper is to present the <i>non–commutative geometrical</i> counterpart of these <i>classical</i> facts within the framework of quantum principal bundles and quantum principal connections.</p>

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Geometry of Associated Quantum Vector Bundles and the Quantum Gauge Group

  • 期刊论文

  • 发表日期：

    2026年5月9日

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  • Gustavo Amilcar Saldaña Moncada

摘要

It is well–known that, given a principal G–bundle equipped with a principal connection, one can associate to every unitary finite–dimensional representation of G a linear connection and a compatible Hermitian structure on the corresponding associated vector bundle. Moreover, the gauge group acts both on the space of principal connections and on the space of induced linear connections defined on the associated vector bundles. The aim of this paper is to present the non–commutative geometrical counterpart of these classical facts within the framework of quantum principal bundles and quantum principal connections.