Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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C* -ALGEBRA OF LOCAL CONJUGACY EQUIVALENCE RELATION ON STRONGLY IRREDUCIBLE SUBSHIFT OF FINITE TYPE

  • Chengjun Hou (School of Mathematical Science Yangzhou University) ;
  • Xiangqi Qiang (School of Mathematics and Physics Jiangsu University of Science and Technology, School of Mathematical Science Yangzhou University)
  • Received : 2023.02.15
  • Accepted : 2023.06.14
  • Published : 2024.01.31
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Abstract

Let G be an infinite countable group and A be a finite set. If Σ ⊆ AG is a strongly irreducible subshift of finite type and 𝓖 is the local conjugacy equivalence relation on Σ. We construct a decreasing sequence 𝓡 of unital C*-subalgebras of C(Σ) and a sequence of faithful conditional expectations E defined on C(Σ), and obtain a Toeplitz algebra 𝓣 (𝓡, 𝓔) and a C*-algebra C*(𝓡, 𝓔) for the pair (𝓡, 𝓔). We show that C*(𝓡, 𝓔) is *-isomorphic to the reduced groupoid C*-algebra C*r(𝓖).

Keywords

Acknowledgement

This work was financially supported by the NSF of China (Grant No. 12271469,11971419).

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