Hecke C*-algebras and semi-direct products

Steven Kaliszewski, Magnus B. Landstad, John Quigg

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We analyse Hecke pairs (G,H) and the associated Hecke algebra H when G is a semi-direct product N ⋊ Q and H = M R for subgroups M N and R Q with M normal in N. Our main result shows that, when (G,H) coincides with its Schlichting completion and R is normal in Q, the closure of Hin C*(G) is MoritaRieffel equivalent to a crossed product IQ/R, where I is a certain ideal in the fixed-point algebra C*(N)R. Several concrete examples are given illustrating and applying our techniques, including some involving subgroups of GL(2,K) acting on K2, where K = or K = [p1]. In particular we look at the ax + b group of a quadratic extension of K.

Original languageEnglish (US)
Pages (from-to)127-153
Number of pages27
JournalProceedings of the Edinburgh Mathematical Society
Volume52
Issue number1
DOIs
StatePublished - Feb 2009

Keywords

  • Group C*-algebra
  • Hecke algebra
  • Morita equivalence
  • Semi-direct product

ASJC Scopus subject areas

  • Mathematics(all)

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