Infinite Non-simple C*-Algebras: Absorbing the Cuntz Algebra O∞
نویسندگان
چکیده
منابع مشابه
Strongly 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 کاملExtensions of representations of the CAR algebra to the Cuntz algebra O 2 — the Fock and the infinite wedge —
(1.1) anam + a ∗ man = δn,mI, a ∗ na ∗ m + a ∗ ma ∗ n = anam + aman = 0 for n, m ∈ N. A0 always has unique C∗-norm ‖ · ‖ and the completion A ≡ A0 with respect to ‖ · ‖ is called the CAR algebra in theory of operator algebras([6]). In [1, 2, 3, 4], we construct several polynomial embeddings of A into the Cuntz algebrasON . For example, if s1, s2 are canonical generators of O2, that is, they sat...
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In this paper we study the problem of when the corona algebra of a non-unital C∗-algebra is purely infinite. A complete answer is obtained for stabilisations of simple and unital algebras that have enough comparison of positive elements. Our result relates the pure infiniteness condition (from its strongest to weakest forms) to the geometry of the tracial simplex of the algebra, and to the beha...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2002
ISSN: 0001-8708
DOI: 10.1006/aima.2001.2041