I am interested in Onsager‘s famous paper “Crystal statistics I” where he derives the solution of the 2D Ising model.
I am reading the original paper, but I search some supplementary material (blog, testbook, paper ect.) where this way (via the Onsager Algebra) of solving the Ising model is explained in other words.
Note that I am NOT interested in the way how Kaufmann solved the model. Even if it is similar.
The letter Onsager Algebra and Integrable Lattice Models, by C. Ahn and K. Shigemoto, might be of interest.
Also, R. J. Baxter's work in Some comments on developments in exact solutions in statistical mechanics since 1944 could prove useful. However, I'm not entirely sure the depth you're seeking in further insights behind Onsager's original paper.
Finally, an alternative approach to the original solution was presented in A Simple Rederivation of Onsager’s Solution of the 2D Ising Model Using Experimental Mathematics, by M. Kauers and D. Zeilberger.
Anyway, hope this helps!