# Higher rank classical analogs of the Askey-Wilson algebra from the $sl_N$ Onsager algebra

Abstract : The $sl_N$-Onsager algebra has been introduced by Uglov and Ivanov in 1995. In this letter, a FRT presentation of the $sl_N$-Onsager algebra is given, its current algebra and commutative subalgebra are constructed. Certain quotients of the $sl_N$-Onsager algebra are then considered, which produce `classical' analogs of higher rank extensions of the Askey-Wilson algebra. As examples, the cases $N=3$ and $N=4$ are described in details.
Document type :
Journal articles
Domain :
Complete list of metadatas

https://hal.archives-ouvertes.fr/hal-01926766
Contributor : L2c Aigle <>
Submitted on : Monday, November 19, 2018 - 2:27:01 PM
Last modification on : Wednesday, November 6, 2019 - 4:12:02 PM

### Identifiers

• HAL Id : hal-01926766, version 1
• ARXIV : 1811.02763

### Citation

Pascal Baseilhac, Nicolas Crampé, Rodrigo A. Pimenta. Higher rank classical analogs of the Askey-Wilson algebra from the $sl_N$ Onsager algebra. Journal of Mathematical Physics, American Institute of Physics (AIP), 2019, 60 (8), pp.081703. ⟨hal-01926766⟩

Record views