Ergodic actions of S_μU(2) on C*-algebras from II_1 subfactors

Details Ergodic actions of S_μU(2) on C*-algebras from II_1 subfactors Ergodic actions of S_μU(2) on C*-algebras from II_1 subfactors

2008-06-27

arxiv.org/abs/0806.4519v4

Mathematics

Operator Algebras

25 pages, references added

Scientific paper

To a proper inclusion N\subset M of II_1 factors of finite Jones index [M:N], we associate an ergodic C*-action of the quantum group S_\mu U(2). The deformation parameter is determined by -1<\mu<0 and [M:N]=|\mu+\mu^{-1}|. The higher relative commutants can be identified with the spectral spaces of the tensor powers of the defining representation of the quantum group. This ergodic action may be thought of as a virtual subgroup of S_\mu U(2) in the sense of Mackey arising from the tensor category generated by M regarded as a bimodule over N. \mu is negative as M is a real bimodule.

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