I want to know the answer to the following question:
What did Lie algebras and hyperbolic quaternions demonstrate a need for?
All the background I'm provided with is that "In a review Alexander Macfarlane wrote: "The main idea of the work is not unification of the several methods, nor generalization of ordinary algebra so as to include them, but rather the comparative study of their several structures."". Is that enough to answer the question?
Answer: no