  The Onsager algebra is one of the cornerstones of exactly solvable models in
statistical mechanics. Starting from the generalised Clifford algebra, we
demonstrate its relations to the graph Temperley-Lieb algebra, and a
generalisation of the Onsager algebra. We present a series of quantum lattice
models as representations of the generalised Clifford algebra, possessing the
structure of a special type of the generalised Onsager algebra. The
integrability of those models is presented, analogous to the free fermionic
eight-vertex model. We also mention further extensions of the models and
physical properties related to the generalised Onsager algebras, hinting at a
general framework that includes families of quantum lattice models possessing
the structure of the generalised Onsager algebras.
