C∗-ALGEBRA OF LOCAL CONJUGACY EQUIVALENCE RELATION ON STRONGLY IRREDUCIBLE SUBSHIFT OF FINITE TYPE
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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).
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).
참고문헌 (10)
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