Geodesic
Poisson–Lie sigma models on Drinfel’d double
Archivum mathematicum, Tome 48 (2012) no. 5, pp. 423-447 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Poisson sigma models represent an interesting use of Poisson manifolds for the construction of a classical field theory. Their definition in the language of fibre bundles is shown and the corresponding field equations are derived using a coordinate independent variational principle. The elegant form of equations of motion for so called Poisson-Lie groups is derived. Construction of the Poisson-Lie group corresponding to a given Lie bialgebra is widely known only for coboundary Lie bialgebras. Using the adjoint representation of Lie group and Drinfel’d double we show that Poisson-Lie group can be constructed for general Lie bialgebra.
Poisson sigma models represent an interesting use of Poisson manifolds for the construction of a classical field theory. Their definition in the language of fibre bundles is shown and the corresponding field equations are derived using a coordinate independent variational principle. The elegant form of equations of motion for so called Poisson-Lie groups is derived. Construction of the Poisson-Lie group corresponding to a given Lie bialgebra is widely known only for coboundary Lie bialgebras. Using the adjoint representation of Lie group and Drinfel’d double we show that Poisson-Lie group can be constructed for general Lie bialgebra.
DOI : 10.5817/AM2012-5-423
Classification : 53D17, 70G45
Keywords: Poisson sigma models; Poisson manifolds; Poisson-Lie groups; bundle maps 
@article{10_5817_AM2012_5_423,
     author = {Vysok\'y, Jan and Hlavat\'y, Ladislav},
     title = {Poisson{\textendash}Lie sigma models on {Drinfel{\textquoteright}d} double},
     journal = {Archivum mathematicum},
     pages = {423--447},
     year = {2012},
     volume = {48},
     number = {5},
     doi = {10.5817/AM2012-5-423},
     mrnumber = {3007623},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.5817/AM2012-5-423/}
}
TY  - JOUR
AU  - Vysoký, Jan
AU  - Hlavatý, Ladislav
TI  - Poisson–Lie sigma models on Drinfel’d double
JO  - Archivum mathematicum
PY  - 2012
SP  - 423
EP  - 447
VL  - 48
IS  - 5
UR  - http://geodesic.mathdoc.fr/articles/10.5817/AM2012-5-423/
DO  - 10.5817/AM2012-5-423
LA  - en
ID  - 10_5817_AM2012_5_423
ER  - 
%0 Journal Article
%A Vysoký, Jan
%A Hlavatý, Ladislav
%T Poisson–Lie sigma models on Drinfel’d double
%J Archivum mathematicum
%D 2012
%P 423-447
%V 48
%N 5
%U http://geodesic.mathdoc.fr/articles/10.5817/AM2012-5-423/
%R 10.5817/AM2012-5-423
%G en
%F 10_5817_AM2012_5_423
Vysoký, Jan; Hlavatý, Ladislav. Poisson–Lie sigma models on Drinfel’d double. Archivum mathematicum, Tome 48 (2012) no. 5, pp. 423-447. doi: 10.5817/AM2012-5-423

Cité par Sources :