ISSN:
1573-0514
Keywords:
K-theory and real rank ofC*-algebras
;
multiplier algebras
;
corona algebras
;
hereditaryC*-subalgebras
;
unitary groups
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract We first determine the homotopy classes of nontrivial projections in a purely infinite simpleC*-algebraA, in the associated multiplier algebraM(A) and the corona algebraM A/A in terms ofK *(A). Then we describe the generalized Fredholm indices as the group of homotopy classes of non-trivial projections ofA; consequently, we determine theK *-groups of all hereditaryC*-subalgebras of certain corona algebras. Secondly, we consider a group structure of *-isomorphism classes of hereditaryC*-subalgebras of purely infinite simpleC*-algebras. In addition, we prove that ifA is aC*-algebra of real rank zero, then each unitary ofA, in caseA it unital, each unitary ofM(A) and ofM(A)/A, in caseA is nonunital but σ-unital, can be factored into a product of a unitary homotopic to the identity and a unitary matrix whose entries are all partial isometries (with respect to a decomposition of the identity).
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00961332
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