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FACTOR MAPS OF LAMBDA-GRAPH SYSTEMS AND INCLUSIONS OF C*-ALGEBRAS

KENGO MATSUMOTO

Department of Mathematical Sciences, Yokohama City University, Seto 22-2, Kanazawa-ku, Yokohama 236-0027, Japan

https://doi.org/10.1142/S0129167X04002351Cited by:1 (Source: Crossref)

Abstract

A λ-graph system is a labeled Bratteli diagram with shift transformation. It is a generalization of finite labeled graphs and presents a subshift. In [Doc. Math. 7 (2002), 1–30], the author introduced a C*-algebra associated with a λ-graph system as a generalization of the Cuntz–Krieger algebras. In this paper, we study a functorial property between factor maps of λ-graph systems and inclusions of the associated C*-algebras with gauge actions. We prove that if there exists a surjective left-covering λ-graph system homomorphism , there exists a unital embedding of the C*-algebra into the C*-algebra compatible to its gauge actions. We also show that a sequence of left-covering graph homomorphisms of finite labeled graphs gives rise to a λ-graph system such that the associated C*-algebra is an inductive limit of the Cuntz–Krieger algebras for the finite labeled graphs.

Keywords:

AMSC: Primary 46L35, Secondary 46L05, Secondary 37B10

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