Letters in Mathematical Physics

, Volume 108, Issue 10, pp 2189–2212 | Cite as

FRT presentation of the Onsager algebras

  • Pascal BaseilhacEmail author
  • Samuel Belliard
  • Nicolas Crampé


A presentation à la Faddeev–Reshetikhin–Takhtajan (FRT) of the Onsager, augmented Onsager and \(sl_2\)-invariant Onsager algebras is given, using the framework of the nonstandard classical Yang–Baxter algebras. Associated current algebras are identified, and generating functions of mutually commuting quantities are obtained.


Onsager algebras Tridiagonal algebra Current algebra Yang–Baxter algebra Integrable systems 

Mathematics Subject Classification

81R50 81R10 81U15 



We thank an anonymous referee for comments. We thank Hubert Saleur and Jasper Stokman for discussions, which motivated the construction of an FRT presentation for the Onsager algebra and its current presentation that could extend to any higher-rank cases. P.B. and N.C. are supported by C.N.R.S. S.B. and N.C. thank the LMPT for hospitality, where part of this work has been done. S.B. is supported by a public grant as part of the Investissement d’avenir project, reference ANR-11-LABX-0056-LMH, LabEx LMH.


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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  • Pascal Baseilhac
    • 1
    Email author
  • Samuel Belliard
    • 2
  • Nicolas Crampé
    • 1
    • 3
  1. 1.Laboratoire de Mathématiques et Physique Théorique CNRS/UMR 7350, Fédération Denis Poisson FR2964Université de ToursToursFrance
  2. 2.Institut de Physique Théorique, DSM, CEA, URA2306CNRS SaclayGif-sur-YvetteFrance
  3. 3.Laboratoire Charles Coulomb (L2C), UMR 5221CNRS-Université de MontpellierMontpellierFrance

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