Skip to main content
placeholder image

An equivalence theorem for reduced Fell bundle C*-algebras

Journal Article


Download full-text (Open Access)

Abstract


  • We show that if E is an equivalence of upper semicontinu-

    ous Fell bundles B and C over groupoids, then there is a linking bundle

    L(E ) over the linking groupoid L such that the full cross-sectional alge-

    bra of L(E ) contains those of B and C as complementary full corners,

    and likewise for reduced cross-sectional algebras. We show how our re-

    sults generalise to groupoid crossed-products the fact, proved by Quigg

    and Spielberg, that Raeburn's symmetric imprimitivity theorem passes

    through the quotient map to reduced crossed products.

UOW Authors


  •   Sims, Aidan
  •   Williams, Dana P. (external author)

Publication Date


  • 2013

Citation


  • Sims, A. & Williams, D. P. (2013). An equivalence theorem for reduced Fell bundle C*-algebras. The New York Journal of Mathematics, 19 159-178.

Scopus Eid


  • 2-s2.0-84883869351

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=2199&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/1190

Number Of Pages


  • 19

Start Page


  • 159

End Page


  • 178

Volume


  • 19

Abstract


  • We show that if E is an equivalence of upper semicontinu-

    ous Fell bundles B and C over groupoids, then there is a linking bundle

    L(E ) over the linking groupoid L such that the full cross-sectional alge-

    bra of L(E ) contains those of B and C as complementary full corners,

    and likewise for reduced cross-sectional algebras. We show how our re-

    sults generalise to groupoid crossed-products the fact, proved by Quigg

    and Spielberg, that Raeburn's symmetric imprimitivity theorem passes

    through the quotient map to reduced crossed products.

UOW Authors


  •   Sims, Aidan
  •   Williams, Dana P. (external author)

Publication Date


  • 2013

Citation


  • Sims, A. & Williams, D. P. (2013). An equivalence theorem for reduced Fell bundle C*-algebras. The New York Journal of Mathematics, 19 159-178.

Scopus Eid


  • 2-s2.0-84883869351

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=2199&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/1190

Number Of Pages


  • 19

Start Page


  • 159

End Page


  • 178

Volume


  • 19