Access to the text (HTML) Access to the text (HTML)
PDF Access to the PDF text

Access to the full text of this article requires a subscription.
  • If you are a subscriber, please sign in 'My Account' at the top right of the screen.

  • If you want to subscribe to this journal, see our rates

  • You can purchase this item in Pay Per ViewPay per View - FAQ : 30,00 € Taxes included to order
    Pages Iconography Videos Other
    5 0 0 0

Comptes Rendus Mathématique
Volume 348, n° 9-10
pages 503-507 (mai 2010)
Doi : 10.1016/j.crma.2010.03.012
accepted : 8 Mars 2010
An algebra of observables for cross ratios
Une algèbre d’observables pour les birapports

François Labourie
Univ. Paris-Sud, laboratoire de mathématiques, CNRS, 91405 Orsay cedex, France 


We define a Poisson Algebra called the swapping algebra using the intersection of curves in the disk. We interpret a subalgebra of the fraction swapping algebra – called the algebra of multifractions – as an algebra of functions on the space of cross ratios and thus as an algebra of functions on the Hitchin component as well as on the space of  -opers with trivial holonomy. We finally relate our Poisson structure to the Drinfel’d–Sokolov structure and to the Atiyah–Bott–Goldman symplectic structure.

The full text of this article is available in PDF format.

Nous introduisons une algèbre de Poisson, l’algèbre d’échange , définie à l’aide de l’intersection des courbes dans le disque. Nous interprétons l’algèbre des multifractions – une sous-algèbre de l’algèbre des fractions de l’algèbre d’échange – comme une algèbre de fonctions sur l’espace des birapports et donc en particulier comme une algèbre de fonctions sur la composante de Hitchin ainsi que sur l’espace des  -opers d’holonomie triviale. Nous relions alors notre structure de Poisson à la structure de Poisson de Drinfel’d–Sokolov ainsi qu’à la structure symplectique d’Atiyah–Bott–Goldman.

The full text of this article is available in PDF format.

 Partially supported by the ANR program ETTT-ANR-09-BLAN-0116-01 and the ANR program RepSurfaces-ANR-06-BLAN-0311.

© 2010  Académie des sciences@@#104156@@
EM-CONSULTE.COM is registrered at the CNIL, déclaration n° 1286925.
As per the Law relating to information storage and personal integrity, you have the right to oppose (art 26 of that law), access (art 34 of that law) and rectify (art 36 of that law) your personal data. You may thus request that your data, should it be inaccurate, incomplete, unclear, outdated, not be used or stored, be corrected, clarified, updated or deleted.
Personal information regarding our website's visitors, including their identity, is confidential.
The owners of this website hereby guarantee to respect the legal confidentiality conditions, applicable in France, and not to disclose this data to third parties.
Article Outline
You can move this window by clicking on the headline