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March 25, 2015 By

On AF embeddability of continuous fields

C. R. Math. Rep. Acad. Sci. Canada Vol. 31 (1) 2009, pp. 16–19

March 30, 2009

Marius Dadarlat, Department of Mathematics, Purdue University, 150 N. University St., West Lafayette, IN, 47907-2067, U.S.A.; email: mdd@math.purdue.edu

Abstract/Résumé:

Let \(A\) be a separable and exact \(C^*\)-algebra which is a continuous field of \(C^*\)-algebras over a connected, locally connected, compact metrizable space. If at least one of the fibers of \(A\) is AF embeddable, then so is \(A\). As an application we show that if \(G\) is a central extension of an amenable and residually finite discrete group by \(\mathbb{Z}^n\), then the \(C^*\)-algebra of \(G\) is AF embeddable.

Soit A une \(C^*\)-algèbre séparable et exacte qui est un champ continu de \(C^*\)-algèbres sur un espace connexe, localement connexe, compact et metrizable. Si au moins l’une des fibres de \(A\) est embeddable dans une AF algèbre donc la \(C^*\)-algèbre \(A\) est aussi. Comme application, nous montrons que si \(G\) est une extension centrale d’un groupe discret amenable et résiduellement fini par le groupe \(\mathbb{Z}^n\), alors la \(C^*\)-algèbre de \(G\) est embeddable dans une AF algèbre.

Keywords: AF algebras, amenable groups, continuous fields of C*-algebras
AMS Subject Classification: General theory of $C^*$-algebras 46L05

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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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