The term "Cartan algebra" has two meanings in mathematics, so care is needed in determining from context which meaning is intended.
One meaning is a "Cartan subalgebra," which is frequently simply called a "torus." This sort of object is common, and means the same thing in all field characteristics.
The other meaning refers to a class of algebras in prime characteristic that are finite-dimensional analogs of some algebras that are infinite-dimensional in characteristic 0 (Seligman 1967).
