On C^(*)-algebras from homoclinic equivalences on subshifts of finite type  

作　　者：Chengjun Hou 

机构地区：[1]School of Mathematical Science,Yangzhou University,Yangzhou 225002,China

出　　处：《Science China Mathematics》2021年第4期747-762,共16页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.11771379,11271224 and 11371290)。

摘　　要：Let G be an infinite countable group and A be a finite set.IfΣ?A~G is a strongly irreducible subshift of finite type,we endow a locally compact and Hausdorff topology on the homoclinic equivalence relation■onΣand show that the reduced C^(*)-algebra C_(r)^(*)(■)of■is a unital simple approximately finite(AF)-dimensional C^(*)-algebra.The shift action G of onΣinduces a canonical automorphism action of G on the C^(*)-algebra C_(r)^(*)(■).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)^(*)(■)is equal to the topology entropy of the shift action of G onΣ.We also establish the variational principle with respect to the noncommutative measure entropy and the topological entropy for the C^(*)-dynamical system(C_(r)^(*)(■),G).

关 键 词：homoclinic equivalence relation groupoid C^(*)-algebra amenable group action entropy 

分 类 号：O177.5[理学—数学]