\(\text{sl}(N)\) Onsager's algebra and integrability.
The authors introduce an \(\text{sl}(N)\) analogue of Onsager's algebra. This is an infinite dimensional Lie algebra, generated by \(N\) elements, \(e_i\), \(i\in \mathbb Z_N\), subject to the relations \([e_i,[e_i,e_{i\pm 1}]]=e_{i\pm 1}\), and \([e_i,e_j]=0\), if \(i-j\neq\pm 1\). An involution in the \(\text{sl}(N)\) loop algebra is defined and the \(\text{sl}(N)\) Onsager algebra is identified with the corresponding fixed point subalgebra. Finally they construct a certain infinite commutative subalgebra.
scientific article; zbMATH DE number 1554022