  Recently, an algebraic generalization of the Jordan-Wigner transformation was
introduced and applied to one- and two-dimensional systems. This transformation
is composed of the interactions $\eta_{i}$ that appear in the Hamiltonian
${\cal H}$ as ${\cal H}=\sum_{i=1}^{N}J_{i}\eta_{i}$, where $J_{i}$ are
coupling constants. In this short note, it is derived that operators that are
composed of $\eta_{i}$, or its $n$-state clock generalizations, generate the
Onsager algebra, which was introduced in the original solution of the
rectangular Ising model, and appears in some integrable models.
