Inductive Limit Algebras from Periodic Weighted Shifts on Fock Space
نویسنده
چکیده
Noncommutative multivariable versions of weighted shift operators arise naturally as ‘weighted’ left creation operators acting on the Fock space Hilbert space. We identify a natural notion of periodicity for these N tuples, and then find a family of inductive limit algebras determined by the periodic weighted shifts which can be regarded as noncommutative multivariable generalizations of the Bunce-Deddens C∗-algebras. We establish this by proving that the C∗-algebras generated by shifts of a given period are isomorphic to full matrix algebras over Cuntz-Toeplitz algebras. This leads to an isomorphism theorem which parallels the Bunce-Deddens and UHF classification scheme.
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