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- Publisher
- Springer Journals
- Copyright
- Copyright © 1994 by Sociedade Brasileira de Matemática
- Subject
- Mathematics; Mathematics, general; Theoretical, Mathematical and Computational Physics
- ISSN
- 1678-7544
- eISSN
- 1678-7714
- DOI
- 10.1007/BF01321306
- Publisher site
- See Article on Publisher Site
Abstract
We describe both the Bunce-DeddensC *-algebras and their Toeplitz versions, as crossed products of commutativeC *-algebras by partial automorphisms. In the latter case, the commutative algebra has, as its spectrum, the union of the Cantor set and a copy of the set of natural numbers ℕ, fitted together in such a way that ℕ is an open dense subset. The partial automorphism is induced by a map that acts like the odometer map on the Cantor set while being the translation by one on ℕ. From this we deduce, by taking quotients, that the Bunce-DeddensC *-algebras are isomorphic to the (classical) crossed product of the algebra of continuous functions on the Cantor set by the odometer map.
Journal
Bulletin of the Brazilian Mathematical Society, New Series – Springer Journals
Published: Mar 3, 2005