Localization \(C^*-\)algebras and index pairing

IF 0.7 4区数学 Q2 MATHEMATICS Journal of Homotopy and Related Structures Pub Date : 2022-11-24 DOI:10.1007/s40062-022-00320-z

Hang Wang, Chaohua Zhang, Dapeng Zhou

引用次数: 0

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.

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定位\(C^*-\)代数和索引配对

对于一对\(C^*\) -代数\((A,\,B)\)的Kasparov kk理论可以用dadarlatt - willett - wu的Yu的局部代数的k理论等价地表示。我们研究了k理论\(K_j(A)\)与kk理论的两个概念(Kasparov kk理论\(KK_i(A,B)\)和\(KK_i(A,B)\)的局部代数描述)之间的配对，并证明了这两个配对是相容的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Homotopy and Related Structures MATHEMATICS-

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Journal of Homotopy and Related Structures (JHRS) is a fully refereed international journal dealing with homotopy and related structures of mathematical and physical sciences. Journal of Homotopy and Related Structures is intended to publish papers on Homotopy in the broad sense and its related areas like Homological and homotopical algebra, K-theory, topology of manifolds, geometric and categorical structures, homology theories, topological groups and algebras, stable homotopy theory, group actions, algebraic varieties, category theory, cobordism theory, controlled topology, noncommutative geometry, motivic cohomology, differential topology, algebraic geometry.

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