THE STABLE EXOTIC CUNTZ ALGEBRAS ARE HIGHER-RANK GRAPH ALGEBRAS

for each odd integer n ≥ 3, we construct a rank-3 graph Λ_n with involution γ_n whose real C*-algebra C*_ℝ (Λ_n,γ_n) is stably isomorphic to the exotic Cuntz algebra ε_n. This construction is optimal, as we prove that a rank-2 graph with involution (Λ,γ) can never satisfy C*_ℝ (Λ,γ) ~_ME ε_n, 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 C_ℝ ^* (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.