Foundations of ktheory for c*algebras

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Title 
Foundations of ktheory for c*algebras 
Author 
Hilgert, Joachim 
School 
Tulane University 
Academic Field 
Mathematics 
Abstract 
Let X be a compact space and Y a closed subset of X. For M(,k), the complex k x kmatrices, consider the C*algebra of continuous functions f : X (>) M(,k) with the property that f(x) is a diagonal matrix for all x (ELEM) Y. We shall study the Ktheory of this C*algebra and some closely related C*algebras for various spaces X and Y. The tools used in this study are a MayerVietoris Sequence and a Puppe Sequence for Ktheory of C*algebras, both of which reduce to the respective sequence in Ktheory of locally compact spaces if the involved C*algebras are commutative First we set up Ktheory of unital C*algebras, following the approach of Karoubi. We define relative Kgroups K(,(alpha))((phi)) for unital C*morphisms (phi) and prove two excision theorems, which will allow us to define Ktheory of nonunital C*algebras. Moreover, we show that the Kfunctors do not distinguish between homotopic C*morphisms. This will enable us to define K(,n) of a C*algebra for all n (ELEM) and to establish a long exact sequence in Ktheory associated to a short exact sequence of C*algebras. We also define a cup product in Ktheory of C*algebras, which will be a (,2)graded bilinear map K(,*)(A) x K(,*)(B) (>) K(,*)(A(' )(CRTIMES)(' )B), give some of its basic properties, and use it to define module structures on the Kgroups Finally we prove a noncommutative splitting principle which generalizes the well known splitting principle for vector bundles over compact spaces 
Language 
eng 
Degree Date 
1982 
Degree 
Ph.D 
Publisher 
Tulane University 
Publication Date 
1982 
Source 
123 p., Dissertation Abstracts International, Volume: 4303, Section: B, page: 0749 
Identifier 
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Copyright is in accordance with U.S. Copyright law 
Contact Information 
digitallibrary@tulane.edu 
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