C*‐algebras for categories of paths associated to the Baumslag–Solitar groups
C*‐algebras for categories of paths associated to the Baumslag–Solitar groups
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与 Baumslag-Solitar 群相关的路径类别的 C*-代数
DOI：
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发表时间：
2011
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通讯作者：
J. Spielberg
中科院分区：
文献类型：
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作者：
J. Spielberg
在本文中，我们描述了与Baumslag-Solitar群相关联的C*-代数，其序由通常的表示定义。这些是森田等价于通过让群作用在其有向边界上获得的交叉积C*-代数。我们用路范畴的方法来定义代数，并推导出生成元和关系的表示。我们得到了Toeplitz代数的完整描述，并计算了Cuntz-Kreiger代数的K-理论。
In this paper, we describe the C*‐algebras associated to the Baumslag–Solitar groups with the ordering defined by the usual presentations. These are Morita equivalent to the crossed product C*‐algebras obtained by letting the group act on its directed boundary. We use the method of categories of paths to define the algebras, and to deduce the presentation by generators and relations. We obtain a complete description of the Toeplitz algebras, and we compute the K‐theory of the Cuntz–Kreiger algebras.