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Ideal structure of uniform Roe algebras of coarse spaces by Xiaoman Chen; Qin Wang is a Mathematics article available to read on EtoBox.

What is Ideal structure of uniform Roe algebras of coarse spaces about?

Let C Ã u ðX ; EÞ be the uniform Roe algebra of a coarse space ðX ; EÞ with uniformly locally finite coarse structure. By a controlled truncation technique, we show that the controlled propagation operators in an ideal I of C Ã u ðX ; EÞ are exactly the controlled truncations of elements in I: It follows that the lattice of the ideals of the uniform Roe algebra C Ã u ðX ; EÞ in which controlled propagation operators are dense, the lattice of the invariant open subsets in the unit space of the groupoid GðX Þ introduced by Skandalis, Tu and Yu, the lattice of the ideals of the coarse structure E; and the lattice of the ideals of the coarse space X are mutually isomorphic. These lattices also give rise to a type of classification for the ideals of C Ã u ðX ; EÞ:

Who reads Ideal structure of uniform Roe algebras of coarse spaces?

Author

Xiaoman Chen; Qin Wang

Publisher

Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0022-1236)

Published

2004

Language

EN

Field

Mathematics (Physical Sciences)