Journal of Noncommutative Geometry

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Volume 12, Issue 3, 2018, pp. 1199–1225
DOI: 10.4171/JNCG/301

Published online: 2018-10-30

On invariants of C*-algebras with the ideal property

Kun Wang[1]

(1) Texas A&M University, College Station, USA and University of Puerto Rico, Rio Piedras, USA

In this paper, we study the relation between the extended Elliott invariant and the Stevens invariant of C*-algebras. We show that in general the Stevens invariant can be derived from the extended Elliott invariant in a functorial manner. We also show that these two invariants are isomorphic for C*-algebras satisfying the ideal property. A C*-algebra is said to have the ideal property if each of its closed two-sided ideals is generated by projections inside the ideal. Both simple, unital C*-algebras and real rank zero C*-algebras have the ideal property. As a consequence, many classes of non-simple C*-algebras can be classified by their extended Elliott invariants, which is a generalization of Elliott’s conjecture.

Keywords: Classification of C*-algebras, ideal property, extended Elliott invariant, Stevens invariant

Wang Kun: On invariants of C*-algebras with the ideal property. J. Noncommut. Geom. 12 (2018), 1199-1225. doi: 10.4171/JNCG/301