A Dixmier–Douady theory for strongly self-absorbing $C^\ast$-algebras II: the Brauer group
نویسندگان
چکیده
منابع مشابه
On 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 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 کاملBrauer Algebras and the Brauer Group
An algebra is a vector space V over a field k together with a kbilinear product of vectors under which V is a ring. A certain class of algebras, called Brauer algebras algebras which split over a finite Galois extension appear in many subfields of abstract algebra, including K-theory and class field theory. Beginning with a definition of the the tensor product, we define and study Brauer algebr...
متن کاملLocalizing the Elliott Conjecture at Strongly Self-absorbing C-algebras, II —–An Appendix
This note provides some technical support to the proof of a result of W. Winter which shows that two unital separable simple amenable Z-absorbing C∗-algebras with locally finite decomposition property satisfying the UCT whose projections separate the traces are isomorphic if their K-theory is finitely generated and their Elliott invariants are the same.
متن کاملTrivialization of C(x)-algebras with Strongly Self-absorbing Fibres
Suppose A is a separable unital C(X)-algebra each fibre of which is isomorphic to the same strongly self-absorbing and K1-injective C∗-algebra D. We show that A and C(X) ⊗ D are isomorphic as C(X)-algebras provided the compact Hausdorff space X is finite-dimensional. This statement is known not to extend to the infinite-dimensional case.
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ژورنال
عنوان ژورنال: Journal of Noncommutative Geometry
سال: 2015
ISSN: 1661-6952
DOI: 10.4171/jncg/218