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Coaction functors, II
- Source :
- Pacific Journal of Mathematics
- Publication Year :
- 2017
-
Abstract
- In further study of the application of crossed-product functors to the Baum-Connes Conjecture, Buss, Echterhoff, and Willett introduced various other properties that crossed-product functors may have. Here we introduce and study analogues of these properties for coaction functors, making sure that the properties are preserved when the coaction functors are composed with the full crossed product to make a crossed-product functor. The new properties for coaction functors studied here are functoriality for generalized homomorphisms and the correspondence property. We particularly study the connections with the ideal property. The study of functoriality for generalized homomorphisms requires a detailed development of the Fischer construction of maximalization of coactions with regard to possibly degenerate homomorphisms into multiplier algebras. We verify that all "KLQ" functors arising from large ideals of the Fourier-Stieltjes algebra $B(G)$ have all the properties we study, and at the opposite extreme we give an example of a coaction functor having none of the properties.<br />minor revisions
- Subjects :
- Exact sequence
Pure mathematics
Conjecture
Functor
Mathematics::Operator Algebras
General Mathematics
010102 general mathematics
Mathematics - Operator Algebras
01 natural sciences
Mathematics::Algebraic Topology
Multiplier (Fourier analysis)
Crossed product
Development (topology)
Mathematics::K-Theory and Homology
Mathematics::Category Theory
0103 physical sciences
Primary 46L55, Secondary 46M15
FOS: Mathematics
Homomorphism
010307 mathematical physics
Ideal (ring theory)
0101 mathematics
Operator Algebras (math.OA)
Mathematics
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Journal :
- Pacific Journal of Mathematics
- Accession number :
- edsair.doi.dedup.....0fe676ad8e9980818a6f006612f2d496