Communications in Mathematical Physics

, Volume 285, Issue 2, pp 537–565 | Cite as

The Classical r-Matrix of AdS/CFT and its Lie Bialgebra Structure

  • Niklas Beisert
  • Fabian Spill
Open Access


In this paper we investigate the algebraic structure of AdS/CFT in the strong-coupling limit. We propose an expression for the classical r-matrix with (deformed) \({\mathfrak{u}(2|2)}\) symmetry, which leads to a quasi-triangular Lie bialgebra as the underlying symmetry algebra. On the fundamental representation our r-matrix coincides with the classical limit of the quantum R-matrix.


Central Charge Hopf Algebra Classical Limit Evaluation Representation Loop Algebra 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


We would like to thank Valentina Forini, Peter Koroteev, Tristan McLoughlin, Jan Plefka, Alessandro Torrielli and the CMP referee for interesting discussions and useful comments.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution,and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2008

Authors and Affiliations

  1. 1.Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-InstitutPotsdamGermany
  2. 2.Institut für PhysikHumboldt-Universität zu BerlinBerlinGermany

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