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| IDEAL STRUCTURE OF UNIFORM ROE ALGEBRAS OVER SIMPLE CORES |
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Citation： |
CHEN Xiaoman,WANG Qin.IDEAL STRUCTURE OF UNIFORM ROE ALGEBRAS OVER SIMPLE CORES[J].Chinese Annals of Mathematics B,2004,25(2):225~232 |
| Page view： 1272
Net amount： 910 |
Authors： |
CHEN Xiaoman; WANG Qin |
Foundation： |
Project supported by the 973 Project of the Ministry of Science and Technology of China, the National
Natural Science Foundation of China (No.10201007), the Doctoral Programme Foundation of the
Ministry of Education of China and the Shanghai Science and Technology Commission (No.01ZA14003). |
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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 $\omega$-filters on $X$, the maximal ideals of
$B^*(X)$ are completely described by the corona of the
Stone-\v{C}ech compactification of $X$. |
Keywords： |
Uniform Roe algebra, Simple core, Ideal, Ultrafilter, Stone-Cech compactification |
Classification： |
46L80 |
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