Inductive limit algebras from periodic weighted shifts on Fock space

Details Inductive limit algebras from periodic weighted shifts on Fock space Inductive limit algebras from periodic weighted shifts on Fock space

2004-11-23

arxiv.org/abs/math/0411520v1

New York J. Math. 8 (2002), 145-159

Mathematics

Operator Algebras

18 pages, preprint version. Paper can also be found at http://nyjm.albany.edu:8000/j/2002/8-9.pdf

Scientific paper

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.

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