On the equi-nuclearity of Roe algebras of metric spaces

Xiaoman Chen; Benyin Fu; Qin Wang

doi:10.1007/s11401-010-0588-1

On the equi-nuclearity of Roe algebras of metric spaces

Xiaoman Chen
, Benyin Fu
, Qin Wang^*

^*Corresponding author for this work

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

Abstract

The authors define the equi-nuclearity of uniform Roe algebras of a family of metric spaces. For a discrete metric space X with bounded geometry which is covered by a family of subspaces {X_i}_i=1^∞, if {C_u^*(X_i)}_i=1^∞ are equi-nuclear and under some proper gluing conditions, it is proved that C_u^*(X) is nuclear. Furthermore, it is claimed that in general, the coarse Roe algebra C^*(X) is not nuclear.

Original language	English
Pages (from-to)	519-528
Number of pages	10
Journal	Chinese Annals of Mathematics. Series B
Volume	31
Issue number	4
DOIs	https://doi.org/10.1007/s11401-010-0588-1
State	Published - 2010
Externally published	Yes

Keywords

Equi-nuclear uniform Roe algebra
Nuclear C-algebra
Uniform Roe algebra

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abstract = "The authors define the equi-nuclearity of uniform Roe algebras of a family of metric spaces. For a discrete metric space X with bounded geometry which is covered by a family of subspaces \{Xi\}i=1∞, if \{Cu*(Xi)\}i=1 ∞ are equi-nuclear and under some proper gluing conditions, it is proved that Cu*(X) is nuclear. Furthermore, it is claimed that in general, the coarse Roe algebra C*(X) is not nuclear.",

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author = "Xiaoman Chen and Benyin Fu and Qin Wang",

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AB - The authors define the equi-nuclearity of uniform Roe algebras of a family of metric spaces. For a discrete metric space X with bounded geometry which is covered by a family of subspaces {Xi}i=1∞, if {Cu*(Xi)}i=1 ∞ are equi-nuclear and under some proper gluing conditions, it is proved that Cu*(X) is nuclear. Furthermore, it is claimed that in general, the coarse Roe algebra C*(X) is not nuclear.

KW - Equi-nuclear uniform Roe algebra

KW - Nuclear C-algebra

KW - Uniform Roe algebra

UR - https://www.scopus.com/pages/publications/77955515332

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DO - 10.1007/s11401-010-0588-1

M3 - 文章

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EP - 528

JO - Chinese Annals of Mathematics. Series B

JF - Chinese Annals of Mathematics. Series B

IS - 4

ER -

On the equi-nuclearity of Roe algebras of metric spaces

Abstract

Keywords

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