论文信息 - A class ofC*-algebras and topological Markov chains

A class ofC*-algebras and topological Markov chains

In this paper we present a class of C*-algebras and point out its close relationship to topological Markov chains, whose theory is part of symbolic dynamics. The C*-algebra construction starts from a matrix A =(A (i,j))i,~ z, Z a finite set, A(i,j)c{0, l}, and where every row and every column of A is non-zero. (That A(i,j)e{O, 1} is assumed for convenience only. All constructions and results extend to matrices with entries in 2~+. We comment on this in Remark 2.18.) A C*-algebra 6~ A is then generated by partial isometries Si~O(i~X ) that act on a Hilbert space in such a way that their support projections Qi=S*S~ and their range projections P~ =SIS* satisfy the relations

Wolfgang Krieger | Wolfgang Krieger | Joachim Cuntz | J. Cuntz

[1] Joachim Cuntz,et al. SimpleC*-algebra generated by isometries , 1977 .

[2] W. L. Paschke,et al. Matrix algebras over $O_n$. , 1979 .

[3] Automorphisms of Certain Simple C*-algebras , 1980 .

[4] G. Pedersen. C-Algebras and Their Automorphism Groups , 1979 .

[5] George A. Elliott,et al. On the classification of inductive limits of sequences of semisimple finite-dimensional algebras , 1976 .

[6] O. Bratteli. Inductive limits of finite dimensional C*-algebras , 1972 .

[7] Lawrence G. Brown,et al. Stable isomorphism of hereditary subalgebras of $C^*$-algebras. , 1977 .

[8] R. F. Williams. Classification of subshifts of finite type , 1973 .

[9] Dennis Sullivan,et al. A topological invariant of flows on 1-dimensional spaces , 1975 .

[10] Wolfgang Krieger. On dimension functions and topological Markov chains , 1980 .

[11] Wolfgang Krieger. On a dimension for a class of homeomorphism groups , 1980 .

[12] John Franks,et al. Homology for zero-dimensional nonwandering sets , 1977 .

[13] W. Arveson. Notes on extensions of $C^*$-algebras , 1977 .

[14] K. Sigmund,et al. Ergodic Theory on Compact Spaces , 1976 .