Cartan Algebra

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).

See also

Cartan Subalgebra, Simple Lie Algebra

This entry contributed by Skip Garibaldi

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Seligman, G. B. Modular Lie Algebras. Berlin: Springer-Verlag, 1967.

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Cartan Algebra

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Garibaldi, Skip. "Cartan Algebra." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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