Fetching the paper…

Reading the bibliography…

2012

Formulation of gauge theories on transitive Lie algebroids

Fournel, Cédric, Lazzarini, Serge, Masson, Thierry

Original
PDF
Post on X

Understand

In this paper we introduce and study some mathematical structures on top of transitive Lie algebroids in order to formulate gauge theories in terms of generalized connections and their curvature: metrics, Hodge star operator and integration along the algebraic part of the transitive Lie algebroid (its kernel).

Explicit action functionals are given in terms of global objects and in terms of their local description as well.
We investigate applications of these constructions to Atiyah Lie algebroids and to derivations on a vector bundle.
The obtained gauge theories are discussed with respect to ordinary and to similar non-commutative gauge theories.

Formulation of gauge theories on transitive Lie algebroids · Around

Built on

Generalization of the Kaluza-Klein theory for an arbitrary nonabelian gauge group
R. Kerner · 1968
Earlier work this paper cites.
Groupes et algèbres de Lie, Chapitres 2 et 3
N. Bourbaki · 1972
Earlier work this paper cites.
Vector fields and generalized vector fields on fibered manifolds
Y. Kosmann-Schwarzbach · 1980
Earlier work this paper cites.
Fibre integral in regular Lie algebroids
J. Kubarski · 1996
Earlier work this paper cites.
Foundations of Differential Geometry, vol. 1
S. Kobayashi and K. Nomizu · 1996
Earlier work this paper cites.

Similar

S U ( n ) {SU}(n) -connections and noncommutative differential geometry
M. Dubois-Violette and T. Masson · 1998
Cited alongside, same era.
On the noncommutative geometry of the endomorphism algebra of a vector bundle
T. Masson · 1999
Cited alongside, same era.
Poincaré duality for transitive unimodular invariantly oriented Lie algebroids
J. Kubarski · 2002
Cited alongside, same era.
Lie algebroids: spectral sequences and signature
J. Kubarski and A. S. Mishchenko · 2003
Cited alongside, same era.

Then

General Theory of Lie Groupoids and Lie Algebroids
K. Mackenzie · 2005
Later among the works it cites.
Noncommutative generalization of S U ( n ) {SU}(n) -principal fiber bundles: a review
T. Masson · 2008
Later among the works it cites.
Gauge theories in noncommutative geometry
T. Masson · 2012
Closest in time.
Connections on Lie algebroids and on derivation-based non-commutative geometry
S. Lazzarini and T. Masson · 2012
Closest in time.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…