%0 Journal Article %T FRT presentation of the Onsager algebras %+ Laboratoire de Mathématiques et Physique Théorique (LMPT) %+ Institut de Physique Théorique - UMR CNRS 3681 (IPHT) %+ Laboratoire Charles Coulomb (L2C) %A Baseilhac, Pascal %A Belliard, Samuel %A Crampé, Nicolas %< avec comité de lecture %@ 0377-9017 %J Letters in Mathematical Physics %I Springer Verlag %V 108 %N 10 %P 2189-2212 %8 2018-10 %D 2018 %Z 1709.08555 %R 10.1007/s11005-018-1068-x %K Onsager algebras %K Integrable systems %K Yang-Baxter algebra %K Tridiagonal algebra %K Current algebra %Z MSC: 81R50; 81R10; 81U15. %Z Mathematics [math]/Mathematical Physics [math-ph]Journal articles %X 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 non-standard classical Yang-Baxter algebras. Associated current algebras are identified, and generating functions of mutually commuting quantities are obtained. %G English %2 https://hal.science/hal-02154881/document %2 https://hal.science/hal-02154881/file/1709.08555%281%29.pdf %L hal-02154881 %U https://hal.science/hal-02154881 %~ CEA %~ UNIV-TOURS %~ CNRS %~ INSMI %~ L2C %~ LMPT %~ DSM-IPHT %~ CEA-UPSAY %~ TDS-MACS %~ UNIV-PARIS-SACLAY %~ CEA-UPSAY-SACLAY %~ MIPS %~ UNIV-MONTPELLIER %~ IDP %~ CEA-DRF %~ TEST-HALCNRS %~ ANR %~ GS-MATHEMATIQUES %~ GS-PHYSIQUE %~ UM-2015-2021 %~ TEST3-HALCNRS