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$\ast $-Homomorphisms of matrix algebras over pseudo-solenoids that are approximated by $\ast $-isomorphisms

Volume 173 / 2023

Kazuhiro Kawamura Colloquium Mathematicum 173 (2023), 211-226 MSC: Primary 46L80; Secondary 55M25, 46L85, 54F15. DOI: 10.4064/cm8862-2-2023 Published online: 26 May 2023


A pseudo-solenoid is a compact connected metrizable space that is an inverse limit of circles and has a characteristic feature, called hereditary indecomposability. The class of pseudo-solenoids has a topological rigidity in that two pseudo-solenoids $X$ and $Y$ are homeomorphic if and only if their first integral Čech cohomology groups are isomorphic. We show that the class of matrix algebras over pseudo-solenoids has a similar rigidity: two matrix algebras $M_{n}(C(X))$ and $M_{n}(C(Y))$ are isomorphic as $C^\ast $-algebras if and only if they have isomorphic $K_1$-groups.


  • Kazuhiro KawamuraDepartment of Mathematics
    University of Tsukuba
    Tsukuba, Ibaraki, 305-8571 Japan

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