On C*-algebras from homoclinic equivalences on subshifts of finite type
| Autor: | Chengjun Hou |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Mathematics::Operator Algebras
General Mathematics 010102 general mathematics Amenable group Hausdorff space Topological entropy Subshift of finite type Automorphism 01 natural sciences Noncommutative geometry Combinatorics 0103 physical sciences Equivalence relation 010307 mathematical physics Locally compact space 0101 mathematics Mathematics |
| Zdroj: | Science China Mathematics. 64:747-762 |
| ISSN: | 1869-1862 1674-7283 |
| DOI: | 10.1007/s11425-018-9421-2 |
| Popis: | Let G be an infinite countable group and A be a finite set. If ∑ ⊆ AG is a strongly irreducible subshift of finite type, we endow a locally compact and Hausdorff topology on the homoclinic equivalence relation ${\cal G}$ on ∑ and show that the reduced C*-algebra $C_r^*\left({\cal G} \right)$ of ${\cal G}$ is a unital simple approximately finite (AF)-dimensional C*-algebra. The shift action of G on ∑ induces a canonical automorphism action of G on the C*-algebra $C_r^*\left({\cal G} \right)$ . We give the notion of noncommutative dynamical entropy invariants for amenable group actions on C*-algebras, and show that, if G is an amenable group, then the noncommutative topological entropy of the canonical automorphism action of G on $C_r^*\left({\cal G} \right)$ is equal to the topology entropy of the shift action of G on ∑. We also establish the variational principle with respect to the noncommutative measure entropy and the topological entropy for the C*-dynamical system ( $C_r^*\left({\cal G} \right)$ , G). |
| Databáze: | OpenAIRE |
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