The Jiang-Su algebra is strongly self-absorbing revisited
نویسندگان
چکیده
We give a shorter proof of the fact that Jiang-Su algebra is strongly self-absorbing. This achieved by introducing and studying so-called unitarily suspended endomorphisms generalized dimension drop algebras. Along way we prove uniqueness existence results for maps between algebras UHF-algebras.
منابع مشابه
The Rohlin property for automorphisms of the Jiang-Su algebra
For projectionless C∗-algebras absorbing the Jiang-Su algebra tensorially, we study a kind of the Rohlin property for autmorphisms. We show that the crossed products obtained by automorphisms with this Rohlin property also absorb the Jiang-Su algebra tensorially under a mild technical condition on the C∗-algebras. In particular, for the Jiang-Su algebra we show the uniqueness up to outer conjug...
متن کاملA Universal Property for the Jiang-su Algebra
We prove that the infinite tensor power of a unital separable C∗-algebra absorbs the Jiang-Su algebra Z tensorially if and only if it contains, unitally, a subhomogeneous algebra without characters. This yields a succinct universal property for Z in a category so large that there are no unital separable C∗-algebras without characters known to lie outside it. This category moreover contains the ...
متن کاملStrongly Self-absorbing C * -algebras
Say that a separable, unital C *-algebra D ≇ C is strongly self-absorbing if there exists an isomorphism ϕ : D → D ⊗ D such that ϕ and id D ⊗ 1 D are approximately unitarily equivalent *-homomorphisms. We study this class of algebras, which includes the Cuntz algebras O 2 , O∞, the UHF algebras of infinite type, the Jiang–Su algebra Z and tensor products of O∞ with UHF algebras of infinite type...
متن کاملA generalization of the Jiang-Su construction
Let G be a countable abelian group. We construct a unital simple projectionless C∗-algebra A with a unique tracial state, that satisfies (K0(A), [1A]) ∼= (Z, 1), K1(A) ∼= G, A ⊗ Z ∼= A, 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, w...
متن کاملOn the Kk-theory of Strongly Self-absorbing C∗-algebras
Let D and A be unital and separable C∗-algebras; let D be strongly selfabsorbing. It is known that any two unital ∗-homomorphisms from D to A ⊗ D are approximately unitarily equivalent. We show that, if D is also K1-injective, they are even asymptotically unitarily equivalent. This in particular implies that any unital endomorphism of D is asymptotically inner. Moreover, the space of automorphi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2022
ISSN: ['0022-1236', '1096-0783']
DOI: https://doi.org/10.1016/j.jfa.2021.109347