The Bunce-Deddens algebras as crossed products by partial automorphisms
The Bunce-Deddens algebras as crossed products by partial automorphisms
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作为部分自同构的叉积的 Bunce-Deddens 代数
DOI：
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发表时间：
1993
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通讯作者：
R. Exel
中科院分区：
文献类型：
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作者：
R. Exel
我们将Bunce-DeddensC*-代数及其Toeplitz版本描述为可交换c *-代数通过部分自同构的交叉积。在后一种情况下，交换代数的谱是康托尔集和自然数集合的一个副本的并集，它们以这样一种方式拟合在一起，使得_1是一个开密集子集。部分自同构是由一个映射引起的，该映射的作用类似于康托集上的里程表映射，同时在n上平移1。由此我们通过取商推导出，Bunce-DeddensC*-代数同构于由里程表映射的康托集合上连续函数代数的（经典）叉积。
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.