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SUMMARY:N. Christopher Phillips
DTSTART:20201002T133000Z
DTEND:20201002T150000Z
DTSTAMP:20260423T021108Z
UID:WSIPM/11
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/WSIPM/11/">C
 rossed products by automorphisms of C(X\,D)</a>\nby N. Christopher Phillip
 s as part of Western Sydney\, IPM joint workshop on Operator Algebras\n\n\
 nAbstract\nWe consider crossed products of\nthe form $C^* \\bigl( {\\mathb
 b{Z}}\, \\\, C (X\, D)\, \\\, \\alpha \\bigr)$\nin which $D$ is simple\, $
 X$ is compact metrizable\,\n$\\alpha$ induces a minimal homeomorphism $h \
 \colon X \\to X$\,\nand a mild technical assumption holds.\nIn a number of
  examples inaccessible\nvia methods based on finite Rokhlin dimension\,\ne
 ither because $D$ is not ${\\mathcal{Z}}$-stable\nor because $X$ is infini
 te dimensional\,\nwe prove structural properties of the crossed product\,\
 nsuch as (tracial) ${\\mathcal{Z}}$-stability\, stable rank one\,\nreal ra
 nk zero\, and pure infiniteness.\n\nThe method is to find a centrally larg
 e subalgebra\nof the crossed product which is a direct limit of\n``recursi
 ve subhomogeneous algebras over $D$''.\nWith a better understanding of suc
 h direct limits\,\nmany more examples would become accessible.\n\nThis is 
 joint work with Dawn Archey and Julian Buck.\n
LOCATION:https://researchseminars.org/talk/WSIPM/11/
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