Noncommutative Principal Bundles Through Twist Deformation

被引：14

作者：

Aschieri, Paolo ^{[1
,2
]}

Bieliavsky, Pierre ^{[3
]}

Pagani, Chiara ^{[4
]}

Schenkel, Alexander ^{[5
]}

机构：

[1] Univ Piemonte Orientale, Dipartimento Sci & Innovaz Tecnol, Viale T Michel 11, I-15121 Alessandria, Italy

[2] Univ Piemonte Orientale, INFN Torino, Viale T Michel 11, I-15121 Alessandria, Italy

[3] Univ Louvain, Inst Rech Math & Phys, Chemin Cyclotron 2 Bte L7-01-02, B-1348 Louvain La Neuve, Belgium

[4] Georg August Univ Gottingen, Math Inst, Bunsenstr 3-5, D-37073 Gottingen, Germany

[5] Univ Regensburg, Fak Math, D-93040 Regensburg, Germany

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2017年 / 352卷 / 01期

关键词：

HOPF GALOIS EXTENSIONS; QUANTUM GROUPS; CONNECTIONS; ALGEBRAS; GEOMETRY; SPHERES; INSTANTONS; CATEGORIES; BIMODULES; MANIFOLDS;

D O I：

10.1007/s00220-016-2765-x

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We construct noncommutative principal bundles deforming principal bundles with a Drinfeld twist (2-cocycle). If the twist is associated with the structure group then we have a deformation of the fibers. If the twist is associated with the automorphism group of the principal bundle, then we obtain noncommutative deformations of the base space as well. Combining the two twist deformations we obtain noncommutative principal bundles with both noncommutative fibers and base space. More in general, the natural isomorphisms proving the equivalence of a closed monoidal category of modules and its twist related one are used to obtain new Hopf-Galois extensions as twists of Hopf-Galois extensions. A sheaf approach is also considered, and examples presented.

引用

页码：287 / 344

页数：58

共 35 条

[1] R-matrix formulation of the quantum inhomogeneous groups ISOq,r(N) and ISp(q,r)(N) [J].

Aschieri, P ;

Castellani, L .

LETTERS IN MATHEMATICAL PHYSICS, 1996, 36 (02) :197-211

[2] On the noncommutative geometry of twisted spheres [J].

Aschieri, P ;

Bonechi, F .

LETTERS IN MATHEMATICAL PHYSICS, 2002, 59 (02) :133-156

[3] Noncommutative geometry and gravity [J].

Aschieri, Paolo ;

Dimitrijevic, Marija ;

Meyer, Frank ;

Wess, Julius .

CLASSICAL AND QUANTUM GRAVITY, 2006, 23 (06) :1883-1911

[4] Noncommutative connections on bimodules and Drinfeld twist deformation [J].

Aschieri, Paolo ;

Schenkel, Alexander .

ADVANCES IN THEORETICAL AND MATHEMATICAL PHYSICS, 2014, 18 (03) :513-612

[5] Nonassociative geometry in quasi-Hopf representation categories II: Connections and curvature [J].

Barnes, Gwendolyn E. ;

Schenkel, Alexander ;

Szabo, Richard J. .

JOURNAL OF GEOMETRY AND PHYSICS, 2016, 106 :234-255

[6] Nonassociative geometry in quasi-Hopf representation categories I: Bimodules and their internal homomorphisms [J].

Barnes, Gwendolyn E. ;

Schenkel, Alexander ;

Szabo, Richard J. .

JOURNAL OF GEOMETRY AND PHYSICS, 2015, 89 :111-152

[7] Deformation Quantization for Actions of Kahlerian Lie Groups [J].

Bieliavsky, Pierre ;

Gayral, Victor .

MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY, 2015, 236 (1115) :1-+

[8] Quantisation of Twistor Theory by Cocycle Twist [J].

Brain, S. J. ;

Majid, S. .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2008, 284 (03) :713-774

[9] MODULI SPACES OF NON-COMMUTATIVE INSTANTONS: GAUGING AWAY NON-COMMUTATIVE PARAMETERS [J].

Brain, Simon ;

Landi, Giovanni .

QUARTERLY JOURNAL OF MATHEMATICS, 2012, 63 (01) :41-86

[10] QUANTUM GROUP GAUGE-THEORY ON QUANTUM SPACES [J].

BRZEZINSKI, T ;

MAJID, S .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1993, 157 (03) :591-638

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