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AF Embedding of Crossed Products of Certain Graph ${\rm C}^*$-Algebras by Quasi-free Actions
C. R. Math. Rep. Acad. Sci. Canada Vol. 31 (3) 2009, pp. 76–86
Xiaochun Fang (Received: 2008/10/24)

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We introduce the notion of quasi-free action of a locally compact abelian group on a graph \({\rm C}^*\)-algebra of a row-finite directed graph, with respect to a labeling of the edges of the graph by elements of the dual group, which we shall call a labeling map. A sufficient condition for AF embedding is given: if the row-finite directed graph is constructed by possibly attaching 1-loops to a row-finite directed graph each weakly connected component of which is a rooted (possibly infinite) directed tree, and the labeling map is almost proper, then the crossed product can be embedded into an AF algebra.

On introduit la notion d’action quasi-libre d’un groupe localement compact abélien sur la \({\rm C}^*\)-algèbre d’un graphe dirigé dont les rangs sont finis, par rapport à un choix d’étiquettes pour les bords du graphe par éléments du groupe dual, qu’on appellera une application d’étiquette. Une condition suffissante pour que la \({\rm C}^*\)-algèbre soit enfoncée dans une \({\rm C}\)-algèbre AF (c’est-à-dire, limite de \({\rm C}^*\)-algèbres de dimesion finie), est donnée, dans laquelle interviennent et le graphe lui-même et l’application d’étiquette.

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algebraic number theory approximation property automorphisms Bessel functions Boson-fermion correspondence C*-algebra Carmichael number center problem Chebyshev transform classification Classification of simple C*-algebras composition operators continued fractions Cuntz Semigroup elliptic curves fixed point Fourier transform function fields. functoriality general relativity generic property ideals indefinite inner product inductive limits of sub-homogeneous C*- algebras Irrational rotation algebra J-Hermitian matrix K-theory Kahler manifolds L-functions maximal ideal space nonexpansive mapping numerical range orthogonal polynomials Predual space prime number property SP Renormalization rotation algebras Salem number semi-reciprocal polynomials tracially approximate splitting interval algebras unbounded traces uniqueness Weak Markov set Whitney problems

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