The algebra of type II1 subfactors of finite index and the Jones polynomial
نویسنده
چکیده
Abstract The algebraic notions of separable extension and split extension of rings, S ⊂ A, are defined dually. If compatible sections and retracts can be found, A is said to be a finite separable extension of S. Then the endomorphism ring homS(A,A) is a finite separable extension of A with a special cyclic idempotent. This construction may be iterated as in Jones theory. The Jones polynomial is defined and the Jones index is shown to be the Hattori-Stallings rank of a projective module. Examples of this theory come from von Neumann algebras, fields, groups and Galois theory.
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