6,321 research outputs found
Ranks of operators in simple C*-algebras
Let A be a unital simple separable C*-algebra with strict comparison of
positive elements. We prove that the Cuntz semigroup of A is recovered
functorially from the Murray-von Neumann semigroup and the tracial state space
T(A) whenever the extreme boundary of T(A) is compact and of finite covering
dimension. Combined with a result of Winter, we obtain Z \otimes A isomorphic
to A whenever A moreover has locally finite decomposition rank. As a corollary,
we confirm Elliott's classification conjecture under reasonably general
hypotheses which, notably, do not require any inductive limit structure. These
results all stem from our investigation of a basic question: what are the
possible ranks of operators in a unital simple C*-algebra?Comment: 19 pages, no figure
On the Cartan map for crossed products and Hopf-Galois extensions
We study certain aspects of the algebraic K-theory of Hopf-Galois extensions.
We show that the Cartan map from K-theory to G-theory of such an extension is a
rational isomorphism, provided the ring of coinvariants is regular, the Hopf
algebra is finite dimensional and its Cartan map is injective in degree zero.
This covers the case of a crossed product of a regular ring with a finite group
and has an application to the study of Iwasawa modules
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