Strongly self-absorbing 𝐶*-algebras

Say that a separable, unital C ∗ C^* -algebra D ≆ C D C is strongly self-absorbing if there exists an isomorphism φ : D → D ⊗ D φ : D → D ⊗ D such that φ φ and i d D ⊗ 1 D idD ⊗ 1D are approximately unitarily equivalent ∗ * -homomorphisms. We study this class of algebras, which includes the Cuntz algebras O 2 O_2 , O ∞ O∞ , the UHF algebras of infinite type, the Jiang–Su algebra Z Z and tensor products of O