Abstract

We consider inductive sequences of Toeplitz–Cuntz algebras. The connecting homomorphisms of such a sequence are defined by a finite set of sequences of positive integers. We prove that the inductive limit of such a sequence of Toeplitz–Cuntz algebras is isomorphic to the reduced semigroup \(C^*\)-algebra constructed for the unitalization of the free product of a finite family of semigroups of positive rational numbers. We show that the limit of the inductive sequence of Toeplitz–Cuntz algebras defined by a finite set of sequences of positive integers is a simple \(C^*\)-algebra.

中文翻译：

---

Toeplitz-Cuntz 代数的归纳序列的极限

摘要

我们考虑 Toeplitz-Cuntz 代数的归纳序列。这种序列的连接同态由一组有限的正整数序列定义。我们证明了这样一个 Toeplitz-Cuntz 代数序列的归纳极限同构于简化的半群\(C^*\) -代数，该代数是为正有理数半群的有限族的自由积的单元化而构造的。我们证明了由有限正整数序列集定义的 Toeplitz-Cuntz 代数归纳序列的极限是一个简单的\(C^*\) -代数。