Ideal structure of uniform Roe algebras over simple cores

Xiaoman Chen; Qin Wang

doi:10.1142/S0252959904000238

Ideal structure of uniform Roe algebras over simple cores

Xiaoman Chen^*
, Qin Wang

^*Corresponding author for this work

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

3 Scopus citations

Abstract

This paper characterizes ideal structure of the uniform Roe algebra B* (X) over simple cores X. A necessary and sufficient condition for a principal ideal of B* (X) to be spatial is given and an example of non-spatial ideal of B* (X) is constructed. By establishing an one-one correspondence between the ideals of B* (X) and the ω-filters on X, the maximal ideals of B* (X) are completely described by the corona of the Stone-Čech compactification of X.

Original language	English
Pages (from-to)	225-232
Number of pages	8
Journal	Chinese Annals of Mathematics. Series B
Volume	25
Issue number	2
DOIs	https://doi.org/10.1142/S0252959904000238
State	Published - 2004
Externally published	Yes

Keywords

Ideal
Simple core
Stone-Čech compactification
Ultrafilter
Uniform Roe algebra

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abstract = "This paper characterizes ideal structure of the uniform Roe algebra B* (X) over simple cores X. A necessary and sufficient condition for a principal ideal of B* (X) to be spatial is given and an example of non-spatial ideal of B* (X) is constructed. By establishing an one-one correspondence between the ideals of B* (X) and the ω-filters on X, the maximal ideals of B* (X) are completely described by the corona of the Stone-{\v C}ech compactification of X.",

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AB - This paper characterizes ideal structure of the uniform Roe algebra B* (X) over simple cores X. A necessary and sufficient condition for a principal ideal of B* (X) to be spatial is given and an example of non-spatial ideal of B* (X) is constructed. By establishing an one-one correspondence between the ideals of B* (X) and the ω-filters on X, the maximal ideals of B* (X) are completely described by the corona of the Stone-Čech compactification of X.

KW - Ideal

KW - Simple core

KW - Stone-Čech compactification

KW - Ultrafilter

KW - Uniform Roe algebra

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M3 - 文章

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JO - Chinese Annals of Mathematics. Series B

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IS - 2

ER -

Ideal structure of uniform Roe algebras over simple cores

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Keywords

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