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July 3, 2015 By

A Classification of Tracially Approximate Splitting Interval Algebras. III. Uniqueness Theorem and Isomorphism Theorem

C. R. Math. Rep. Acad. Sci. Canada Vol. 37 (2) 2015, pp. 41-75

June 30, 2015

Zhuang Niu,Department of Mathematics, University of Wyoming, Laramie, Wyoming, 82071 USA; e-mail: zniu@uwyo.edu

Abstract/Résumé:

Motivated by Huaxin Lin’s axiomatization of AH-algebras, the class of TASI-algebras is introduced as the class of unital C*-algebras which can be tracially approximated by splitting interval algebras—certain sub-C*-algebras of interval algebras. It is shown that the class of simple separable nuclear TASI-algebras satisfying the UCT is classified by the Elliott invariant. As a consequence, any such TASI-algebra is then isomorphic to an inductive limit of splitting interval algebras together with certain homogeneous C*-algebras—so it is an ASH-algebra.

Une classe de C*-algèbres qui généralisent la classe bien connue TAI de Lin est considérée—basées sur, au lieu de l’intervalle, ce qui pourrait s’appeler l’intervalle fendu ("splitting interval"), de sorte que l'on les appelle la classe TASI. On montre que la classe de C*-algèbres TASI qui sont simples, nucléaires, et à élément unité, qui vérifient le théorème à coefficients universels (UCT), peuvent se classifier d’après l’invariant d’Elliott.

Keywords: Classification of simple C*-algebras, inductive limits of sub-homogeneous C*- algebras, tracially approximate splitting interval algebras
AMS Subject Classification: Classifications of $C^*$-algebras; factors 46L35

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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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