Inductive limit algebras from periodic weighted shifts on Fock space
Abstract
Description
Non-commutative 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 non-commutative 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.
18 pages, preprint version. Paper can also be found at http://nyjm.albany.edu:8000/j/2002/8-9.pdf
18 pages, preprint version. Paper can also be found at http://nyjm.albany.edu:8000/j/2002/8-9.pdf