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

Department of Science and Technological Innovation

Research output: Contribution to journal › Article › 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.

Original language	English
Article number	13
Journal	Mathematical Physics Analysis and Geometry
Volume	26
Issue number	2
DOIs	https://doi.org/10.1007/s11040-023-09454-9
Publication status	Published - Jun 2023

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

Access to Document

10.1007/s11040-023-09454-9

Cite this

@article{0fd6ec1529db4cd7ba213a745626819f,

title = "Braided Hopf Algebras and Gauge Transformations II: ∗ -Structures and Examples",

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{\textendash}Galois extensions, Noncommutative gauge transformations",

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

note = "Publisher Copyright: {\textcopyright} 2023, The Author(s).",

year = "2023",

month = jun,

doi = "10.1007/s11040-023-09454-9",

language = "English",

volume = "26",

journal = "Mathematical Physics Analysis and Geometry",

issn = "1385-0172",

publisher = "Springer Netherlands",

number = "2",

}

TY - JOUR

T1 - Braided Hopf Algebras and Gauge Transformations II

T2 - ∗ -Structures and Examples

AU - Aschieri, Paolo

AU - Landi, Giovanni

AU - Pagani, Chiara

PY - 2023/6

Y1 - 2023/6

N2 - 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.

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

UR - https://www.scopus.com/pages/publications/85159227250

U2 - 10.1007/s11040-023-09454-9

DO - 10.1007/s11040-023-09454-9

M3 - Article

SN - 1385-0172

VL - 26

JO - Mathematical Physics Analysis and Geometry

JF - Mathematical Physics Analysis and Geometry

IS - 2

M1 - 13

ER -

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

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this