The C*-algebra of a vector bundle and fields of Cuntz algebras

被引：12

作者：

Vasselli, E ^{[1
]}

机构：

[1] Univ Roma La Sapienza, Dipartimento Matemat, I-00185 Rome, Italy

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2005年 / 222卷 / 02期

关键词：

Cuntz-Pimsner algebra; Cuntz algebra; continuous field; vector bundle; K-theory;

D O I：

10.1016/j.jfa.2004.09.004

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the Cuntz-Pimsner algebra associated with the module of continuous sections of a Hilbert bundle, and prove that it is a continuous bundle of Cuntz algebras. Furthermore, we assign to bundles of Cuntz algebras carrying a global circle action a class in the representable KK-group of the zero-grade bundle. We explicitly compute such class for the Cuntz-Pimsner algebra of a vector bundle. (c) 2004 Elsevier Inc. All rights reserved.

引用

页码：491 / 502

页数：12

共 50 条

[1] Embedding of continuous fields of C*-algebras in the Cuntz algebra O2
Kirchberg, E
Phillips, NC
[J]. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2000, 525 : 55 - 94
[2] Convex topological algebras via linear vector fields and Cuntz algebras
Bock, Wolfgang
Futorny, Vyacheslav
Neklyudov, Mikhail
[J]. JOURNAL OF PURE AND APPLIED ALGEBRA, 2021, 225 (03)
[3] Extension algebras of Cuntz algebra
Liu, Shudong
Fang, Xiaochun
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 329 (01) : 655 - 663
[4] The C*-algebra of a vector bundle
Dadarlat, Marius
[J]. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2012, 670 : 121 - 143
[5] EXTENSION ALGEBRAS OF CUNTZ ALGEBRA, II
Liu, Shudong
Fang, Xiaochun
[J]. BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2009, 80 (01) : 83 - 90
[6] Symmetries of the C*-algebra of a vector bundle
Deaconu, Valentin
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2021, 494 (02)
[7] Embedding of exact C*-algebras in the Cuntz algebra O2
Kirchberg, E
Phillips, NC
[J]. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2000, 525 : 17 - 53
[8] Infinite non-simple C*-algebras:: Absorbing the Cuntz algebra φ∞
Kirchberg, E
Rordam, M
[J]. ADVANCES IN MATHEMATICS, 2002, 167 (02) : 195 - 264
[9] A topological invariant for continuous fields of Cuntz algebras
Taro Sogabe
[J]. Mathematische Annalen, 2021, 380 : 91 - 117
[10] A topological invariant for continuous fields of Cuntz algebras
Sogabe, Taro
[J]. MATHEMATISCHE ANNALEN, 2021, 380 (1-2) : 91 - 117

← 1 2 3 4 5 →