TY - JOUR

T1 - THE STABLE EXOTIC CUNTZ ALGEBRAS ARE HIGHER-RANK GRAPH ALGEBRAS

AU - Boersema, Jeffrey L.

AU - Browne, Sarah L.

AU - Gillaspy, Elizabeth

N1 - Publisher Copyright:
© 2024, American Mathematical Society. All rights reserved.

PY - 2024

Y1 - 2024

N2 - for each odd integer n ≥ 3, we construct a rank-3 graph Λn with involution γn whose real C*-algebra C*ℝ (Λn,γn) is stably isomorphic to the exotic Cuntz algebra εn. This construction is optimal, as we prove that a rank-2 graph with involution (Λ,γ) can never satisfy C*ℝ (Λ,γ) ~ME εn, and Boersema reached the same conclusion for rank-1 graphs (directed graphs) in [Munster J. Math. 10 (2017), pp. 485-521, Corollary 4.3]. Our construction relies on a rank-1 graph with involution (Λ,γ) whose real C*-algebra Cℝ * (Λ, γ) is stably isomorphic to the suspension Sℝ. In the Appendix, we show that the i-fold suspension Siℝ is stably isomorphic to a graph algebra iff - 2 ≤ i ≤ 1.

AB - for each odd integer n ≥ 3, we construct a rank-3 graph Λn with involution γn whose real C*-algebra C*ℝ (Λn,γn) is stably isomorphic to the exotic Cuntz algebra εn. This construction is optimal, as we prove that a rank-2 graph with involution (Λ,γ) can never satisfy C*ℝ (Λ,γ) ~ME εn, and Boersema reached the same conclusion for rank-1 graphs (directed graphs) in [Munster J. Math. 10 (2017), pp. 485-521, Corollary 4.3]. Our construction relies on a rank-1 graph with involution (Λ,γ) whose real C*-algebra Cℝ * (Λ, γ) is stably isomorphic to the suspension Sℝ. In the Appendix, we show that the i-fold suspension Siℝ is stably isomorphic to a graph algebra iff - 2 ≤ i ≤ 1.

UR - http://www.scopus.com/inward/record.url?scp=85188659348&partnerID=8YFLogxK

U2 - 10.1090/bproc/180

DO - 10.1090/bproc/180

M3 - Article

AN - SCOPUS:85188659348

VL - 11

SP - 47

EP - 62

JO - Proceedings of the American Mathematical Society, Series B

JF - Proceedings of the American Mathematical Society, Series B

ER -