Embedding C∗-algebra extensions into AF algebras
نویسندگان
چکیده
منابع مشابه
Embedding Crossed Products into a Unital Simple AF-algebra
Let X be a compact metric space and let α be a homeomorphism on X. Related to a theorem of Pimsner, we show that C(X) ⋊α Z can be embedded into a unital simple AF-algebra if and only if there is a strictly positive α-invariant Borel probability measure. Suppose that Λ is a Z action on X. If C(X)⋊Λ Z can be embedded into a unital simple AF-algebra, then there must exist a strictly positive Λ-inv...
متن کاملExtensions for Af C* Algebras and Dimension Groups
Let A, C be approximately finite dimensional (AF) C* algebras, with A nonunital and C unital; suppose that either (i) A is the algebra of compact operators, or (ii) both A, C are simple. The classification of extensions of A by C is studied here, by means of Elliott's dimension groups. In case (i), the weak Ext group of C is shown to be Extz( K0(C),Z), and the strong Ext group is an extension o...
متن کاملAF-embedding of crossed products of AH-algebras by Z and asymptotic AF-embedding
Let A be a unital AH-algebra and let α ∈ Aut(A) be an automorphism. A necessary condition for A ⋊α Z being embedded into a unital simple AF-algebra is the existence of a faithful tracial state. If in addition, there is an automorphism κ with κ∗1 = −idK1(A) such that α ◦ κ and κ ◦ α are asymptotically unitarily equivalent, then A⋊α Z can be embedded into a unital simple AF-algebra. Consequently,...
متن کاملEmbedding normed linear spaces into $C(X)$
It is well known that every (real or complex) normed linear space $L$ is isometrically embeddable into $C(X)$ for some compact Hausdorff space $X$. Here $X$ is the closed unit ball of $L^*$ (the set of all continuous scalar-valued linear mappings on $L$) endowed with the weak$^*$ topology, which is compact by the Banach--Alaoglu theorem. We prove that the compact Hausdorff space $X$ can ...
متن کاملHopf Algebra Extensions of Monogenic Hopf Algebras
William M. Singer has described a cohomology theory of connected Hopf algebras which classifies extensions of a cocommutative Hopf algebra by a commutative Hopf algebra in much the same way as the cohomology of groups classifies extensions of a group by an abelian group. We compute these cohomology groups for monogenic Hopf algebras, construct an action of the base ring on the cohomology groups...
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: 1988
ISSN: 0022-1236
DOI: 10.1016/0022-1236(88)90104-8