Braided Hopf Algebras and Gauge Transformations II: ∗ -Structures and Examples

Paolo Aschieri; Giovanni Landi; Chiara Pagani

doi:10.1007/s11040-023-09454-9

Braided Hopf Algebras and Gauge Transformations II: ∗ -Structures and Examples

Paolo Aschieri
, Giovanni Landi
, Chiara Pagani

Dipartimento di Scienze e Innovazione Tecnologica

Risultato della ricerca: Contributo su rivista › Articolo in rivista › peer review

Abstract

We consider noncommutative principal bundles which are equivariant under a triangular Hopf algebra. We present explicit examples of infinite dimensional braided Lie and Hopf algebras of infinitesimal gauge transformations of bundles on noncommutative spheres. The braiding of these algebras is implemented by the triangular structure of the symmetry Hopf algebra. We present a systematic analysis of compatible ∗ -structures, encompassing the quasitriangular case.

Lingua originale	Inglese
Numero di articolo	13
Rivista	Mathematical Physics Analysis and Geometry
Volume	26
Numero di pubblicazione	2
DOI	https://doi.org/10.1007/s11040-023-09454-9
Stato di pubblicazione	Pubblicato - giu 2023

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10.1007/s11040-023-09454-9

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abstract = "We consider noncommutative principal bundles which are equivariant under a triangular Hopf algebra. We present explicit examples of infinite dimensional braided Lie and Hopf algebras of infinitesimal gauge transformations of bundles on noncommutative spheres. The braiding of these algebras is implemented by the triangular structure of the symmetry Hopf algebra. We present a systematic analysis of compatible ∗ -structures, encompassing the quasitriangular case.",

keywords = "-structures, Braided Lie algebras, Braided derivations, Gauge transformations of the instanton bundle, Gauge transformations of the orthogonal bundle on theta 4-sphere, Hopf–Galois extensions, Noncommutative gauge transformations",

author = "Paolo Aschieri and Giovanni Landi and Chiara Pagani",

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AU - Landi, Giovanni

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AB - We consider noncommutative principal bundles which are equivariant under a triangular Hopf algebra. We present explicit examples of infinite dimensional braided Lie and Hopf algebras of infinitesimal gauge transformations of bundles on noncommutative spheres. The braiding of these algebras is implemented by the triangular structure of the symmetry Hopf algebra. We present a systematic analysis of compatible ∗ -structures, encompassing the quasitriangular case.

KW - -structures

KW - Braided Lie algebras

KW - Braided derivations

KW - Gauge transformations of the instanton bundle

KW - Gauge transformations of the orthogonal bundle on theta 4-sphere

KW - Hopf–Galois extensions

KW - Noncommutative gauge transformations

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DO - 10.1007/s11040-023-09454-9

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JO - Mathematical Physics Analysis and Geometry

JF - Mathematical Physics Analysis and Geometry

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ER -

Braided Hopf Algebras and Gauge Transformations II: ∗ -Structures and Examples

Abstract

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