Localization C∗- algebras and index pairing

Hang Wang; Chaohua Zhang; Dapeng Zhou

doi:10.1007/s40062-022-00320-z

Localization C^∗- algebras and index pairing

Hang Wang^*
, Chaohua Zhang
, Dapeng Zhou

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

Kasparov KK-theory for a pair of C^∗-algebras (A,B) can be formulated equivalently in terms of the K-theory of Yu’s localization algebra by Dadarlat-Willett-Wu. We investigate the pairings between K-theory K_j(A) and the two notions of KK-theory which are Kasparov KK-theory KK_i(A, B) and the localization algebra description of KK_i(A, B) and show that the two pairings are compatible.

Original language	English
Pages (from-to)	1-22
Number of pages	22
Journal	Journal of Homotopy and Related Structures
Volume	18
Issue number	1
DOIs	https://doi.org/10.1007/s40062-022-00320-z
State	Published - Mar 2023

Keywords

Index pairing
K-homology
K-theory
KK-theory
Localization algebra

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abstract = "Kasparov KK-theory for a pair of C∗-algebras (A,B) can be formulated equivalently in terms of the K-theory of Yu{\textquoteright}s localization algebra by Dadarlat-Willett-Wu. We investigate the pairings between K-theory Kj(A) and the two notions of KK-theory which are Kasparov KK-theory KKi(A, B) and the localization algebra description of KKi(A, B) and show that the two pairings are compatible.",

keywords = "Index pairing, K-homology, K-theory, KK-theory, Localization algebra",

author = "Hang Wang and Chaohua Zhang and Dapeng Zhou",

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AU - Zhang, Chaohua

AU - Zhou, Dapeng

PY - 2023/3

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N2 - Kasparov KK-theory for a pair of C∗-algebras (A,B) can be formulated equivalently in terms of the K-theory of Yu’s localization algebra by Dadarlat-Willett-Wu. We investigate the pairings between K-theory Kj(A) and the two notions of KK-theory which are Kasparov KK-theory KKi(A, B) and the localization algebra description of KKi(A, B) and show that the two pairings are compatible.

AB - Kasparov KK-theory for a pair of C∗-algebras (A,B) can be formulated equivalently in terms of the K-theory of Yu’s localization algebra by Dadarlat-Willett-Wu. We investigate the pairings between K-theory Kj(A) and the two notions of KK-theory which are Kasparov KK-theory KKi(A, B) and the localization algebra description of KKi(A, B) and show that the two pairings are compatible.

KW - Index pairing

KW - K-homology

KW - K-theory

KW - KK-theory

KW - Localization algebra

UR - https://www.scopus.com/pages/publications/85142625718

U2 - 10.1007/s40062-022-00320-z

DO - 10.1007/s40062-022-00320-z

M3 - 文章

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JO - Journal of Homotopy and Related Structures

JF - Journal of Homotopy and Related Structures

IS - 1

ER -

Localization C^∗- algebras and index pairing

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