The Bunce-Deddens algebras as crossed products by partial automorphisms
- Ruy Exel
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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.
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- The Bunce-Deddens algebras as crossed products by partial automorphisms
Boletim da Sociedade Brasileira de Matemática - Bulletin/Brazilian Mathematical Society
Volume 25, Issue 2 , pp 173-179
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- Ruy Exel (1)
- Author Affiliations
- 1. Departamento de Matemática, Universidade de São Paulo, C. P. 20570, 01452-990, São Paulo, Brazil