A generalization of the Jiang-Su construction

Abstract

Let $G$ be a countable abelian group. We construct a unital simple projectionless C*-algebra $A$ with a unique tracial state, that satisfies $(K_0(A),[1_A])\cong (\mathbb{Z},1)$, $K_1(A)\cong G$, absorbs the Jiang-Su algebra tensorially, and that is obtained as the inductive limit C*-algebra of a sequence of dimension drop algebras of a specific form. This construction is based on the construction of the Jiang-Su algebra. By this construction, we show a certain conjugacy result for aperiodic automorphisms of these projectionless C*-algebras. We also show that an automorphism of this projectoinless C*-algebra has a certain aperiodicity up to the weakly inner automorphisms in the tracial representation if and only if it has a kind of Rohlin property, which leads to the Rohlin property after taking tensor product of certain C*-algebras of real rank zero.

27 pages

References in corpus (4)

• Localizing the Elliott conjecture at strongly self-absorbing C*-algebras
• The Jiang-Su algebra revisited
• Inductive Limits of Subhomogeneous $C^{\ast }$-algebras with Hausdorff Spectrum
• Certain aperiodic automorphisms of unital simple projectionless C*-algebras