Exotic group C*-algebras in noncommutative duality

Steven Kaliszewski, Magnus B. Landstad, John Quigg

Research output: Contribution to journalArticle

14 Scopus citations

Abstract

We show that for a locally compact group G there is a one-to-one correspondence between G-invariant weak*-closed subspaces E of the Fourier-Stieltjes algebra B(G) containing Br(G) and quotients C*E (G) of C*(G) which are intermediate between C*(G) and the reduced group algebra C*r (G). We show that the canonical comultiplication on C*(G) descends to a coaction or a comultiplication on C*E (G) if and only if E is an ideal or subalgebra, respectively. When α is an action of G on a C*-algebra B, we define E-crossed products B ⋊ α,E G lying between the full crossed product and the reduced one, and we conjecture that these intermediate crossed products satisfy an exotic version of crossed-product duality involving C*E (G).

Original languageEnglish (US)
Pages (from-to)689-711
Number of pages23
JournalNew York Journal of Mathematics
Volume19
StatePublished - Nov 7 2013

Keywords

  • C*-bialgebra
  • Coaction
  • Fourier-stieltjes algebra
  • Group C*-algebra
  • Hopf C*-algebra
  • Quantum group

ASJC Scopus subject areas

  • Mathematics(all)

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