Poisson–Lie sigma models on Drinfel’d double

Jan Vysoký; Ladislav Hlavatý

Archivum Mathematicum (2012)

  • Volume: 048, Issue: 5, page 423-447
  • ISSN: 0044-8753

Abstract

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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.

How to cite

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Vysoký, Jan, and Hlavatý, Ladislav. "Poisson–Lie sigma models on Drinfel’d double." Archivum Mathematicum 048.5 (2012): 423-447. <http://eudml.org/doc/251420>.

@article{Vysoký2012,
abstract = {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.},
author = {Vysoký, Jan, Hlavatý, Ladislav},
journal = {Archivum Mathematicum},
keywords = {Poisson sigma models; Poisson manifolds; Poisson-Lie groups; bundle maps; Poisson sigma model; Poisson manifold; Poisson-Lie group; bundle map},
language = {eng},
number = {5},
pages = {423-447},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Poisson–Lie sigma models on Drinfel’d double},
url = {http://eudml.org/doc/251420},
volume = {048},
year = {2012},
}

TY - JOUR
AU - Vysoký, Jan
AU - Hlavatý, Ladislav
TI - Poisson–Lie sigma models on Drinfel’d double
JO - Archivum Mathematicum
PY - 2012
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 048
IS - 5
SP - 423
EP - 447
AB - 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.
LA - eng
KW - Poisson sigma models; Poisson manifolds; Poisson-Lie groups; bundle maps; Poisson sigma model; Poisson manifold; Poisson-Lie group; bundle map
UR - http://eudml.org/doc/251420
ER -

References

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  9. Nakahara, M., Geometry, Topology and Physics, Taylor & Francis, 2003. (2003) Zbl1090.53001MR2001829
  10. Schaller, P., Strobl, T., Poisson–Sigma–Models: A generalization of 2–D gravity Yang–Mills–systems, hep-th/9411163. 
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