Partial translation algebras for certain discrete metric spaces
Partial translation algebras for certain discrete metric spaces
复制标题
某些离散度量空间的部分平移代数
DOI：
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发表时间：
2010
期刊：
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通讯作者：
R. J. Putwain
中科院分区：
文献类型：
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作者：
R. J. Putwain
部分平移代数的概念是由Brodzki，Niblo和Wright在[11]中引入的，以提供度量空间的约化群C*-代数的类似物。这样一个代数是从一个部分翻译结构，结构，任何有界几何一致离散度量空间承认，我们证明了这些结构限制子空间，并保持一致双射，导致一个新的证明现有的定理。我们研究了一些例子的部分翻译结构和代数，他们给出了详细的，特别是研究的情况下，两个不同的代数可能与相同的度量空间。我们介绍的概念之间的映射部分翻译结构，并使用此来描述时，映射的度量空间产生的同态相关的部分翻译代数。利用这个同态，我们构造了一个群的子空间的C*-代数扩张，我们利用它来计算由整数的特定子空间产生的代数的K-理论。我们还研究了由部分平移结构构造广群的方法，并证明了在离散群的情况下，伴随的C*-代数与约化群C*-代数相同.除此之外，我们提出了几个附属的结果有关的部分翻译和cotranslation和运营商，这些引起。
The notion of a partial translation algebra was introduced by Brodzki, Niblo and Wright in [11] to provide an analogue of the reduced group C*-algebra for metric spaces. Such an algebra is constructed from a partial translation structure, a structure which any bounded geometry uniformly discrete metric space admits; we prove that these structures restrict to subspaces and are preserved by uniform bijections, leading to a new proof of an existing theorem. We examine a number of examples of partial translation structures and the algebras they give rise to in detail, in particular studying cases where two different algebras may be associated with the same metric space. We introduce the notion of a map between partial translation structures and use this to describe when a map of metric spaces gives rise to a homomorphism of related partial translation algebras. Using this homomorphism, we construct a C*-algebra extension for subspaces of groups, which we employ to compute K-theory for the algebra arising from a particular subspace of the integers. We also examine a way to form a groupoid from a partial translation structure, and prove that in the case of a discrete group the associated C*-algebra is the same as the reduced group C*-algebra. In addition to this we present several subsidiary results relating to partial translations and cotranslations and the operators these give rise to.