刊名:Journal of Mathematical Analysis and Applications
出版年:2017
出版时间:1 January 2017
年:2017
卷:445
期:1
页码:898-943
全文大小:944 K
文摘
We investigate structural properties of the reduced cross-sectional algebra e4c3cc57e55e"> of a Fell bundle e441e6fdf8c3d0754bf" title="Click to view the MathML source">B over a discrete group G . Conditions allowing one to determine the ideal structure of e4c3cc57e55e"> are studied. Notions of aperiodicity, paradoxicality and e441e6fdf8c3d0754bf" title="Click to view the MathML source">B-infiniteness for the Fell bundle e441e6fdf8c3d0754bf" title="Click to view the MathML source">B are introduced and investigated by themselves and in relation to the partial dynamical system dual to e441e6fdf8c3d0754bf" title="Click to view the MathML source">B. Several criteria of pure infiniteness of e4c3cc57e55e"> are given. It is shown that they generalize and unify corresponding results obtained in the context of crossed products, by the following duos: Laca, Spielberg [34]; Jolissaint, Robertson [21]; Sierakowski, Rørdam [47]; Giordano, Sierakowski [18] and Ortega, Pardo [39]. For exact, separable Fell bundles satisfying the residual intersection property primitive ideal space of e4c3cc57e55e"> is determined. The results of the paper are shown to be optimal when applied to graph C⁎-algebras. Applications to a class of Exel–Larsen crossed products are presented.