On the classification of simple amenable -algebras with finite decomposition rank, II

  • George A. Elliott

    University of Toronto, Toronto, Canada
  • Guihua Gong

    University of Puerto Rico, San Juan, USA
  • Huaxin Lin

    East China Normal University, Shanghai, P. R. China; University of Oregon, Eugene, USA; Shanghai Institute of Mathematics and Interdisciplinary Sciences, Shanghai, P. R. China
  • Zhuang Niu

    University of Wyoming, Laramie, USA
On the classification of simple amenable $\mathrm{C}^{*}$-algebras with finite decomposition rank, II cover
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Abstract

We prove that every unital simple separable -algebra with finite decomposition rank which satisfies the UCT has the property that has generalized tracial rank at most one, where is the universal UHF-algebra. Consequently, is classifiable in the sense of Elliott.

Cite this article

George A. Elliott, Guihua Gong, Huaxin Lin, Zhuang Niu, On the classification of simple amenable -algebras with finite decomposition rank, II. J. Noncommut. Geom. 19 (2025), no. 1, pp. 73–104

DOI 10.4171/JNCG/560