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<p>In this paper, we study tensor products of finite AW*-algebras and approximately finite-dimensional C*-algebras. In 2014, U.&#xa0;Haagerup proved that any C*-algebra with a quasitrace has a unique AW*-completion, which is a finite AW*-algebra. In this paper, continuing Haagerup’s research, we construct tensor products of a finite AW*-algebra by approximately finite-dimensional algebras that are nonisomorphic as C*-algebras (i.e., their uniform completions are nonisomorphic), and their completions with respect to the metric generated by the corresponding quasitraces are isomorphic as AW*-algebras.</p>

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ON THE ISOMORPHISM OF UNIFORMLY APPROXIMATIVE AW*-ALGEBRAS

  • 期刊论文

  • 发表日期：

    2026年2月1日

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  • D. I. Kim,
  • A. A. Rakhimov

摘要

In this paper, we study tensor products of finite AW*-algebras and approximately finite-dimensional C*-algebras. In 2014, U. Haagerup proved that any C*-algebra with a quasitrace has a unique AW*-completion, which is a finite AW*-algebra. In this paper, continuing Haagerup’s research, we construct tensor products of a finite AW*-algebra by approximately finite-dimensional algebras that are nonisomorphic as C*-algebras (i.e., their uniform completions are nonisomorphic), and their completions with respect to the metric generated by the corresponding quasitraces are isomorphic as AW*-algebras.