I could never, for the life of me, recall the definition of a root system in Lie theory. It probably doesn't help that I've never taken a course on Lie Theory - the algebra, or the groups, or the differential geometry - even though I was at one of the best universities at the country.

The definition of a root system, I find - if not others, is easily forgettable. However, recently I discovered that root systems were an example of a quandle, the axioms of which go back to Mituhisa Takasaki in 1942, and simply axiomatise the properties of conjugation in groups. I found this useful nugget in the book, Quandles, An Introduction to the Algebra of Knots by Mohammed Elhamdadi and Sam Nelson.

Would it then, not be useful, to include this in a discussion of Lie algebras and their classification?