On the isomorphism of uniformly approximative AW*-algebras

D. I. Kim^ab, A. A. Rakhimov<sup>a

a</sup> National University of Uzbekistan named after Mirzo Ulugbek, Tashkent
^b Tashkent Branch of Russian University of Economics named after G.V. Plekhanov

Abstract: 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.

Keywords: quasitrace, d$_\tau$-metric, C*-algebra, AW*-algebra, hyperfiniteness

UDC: 517.986

MSC: 46Lxx, 47B47, 47C15

DOI: 10.36535/2782-4438-2025-245-59-64