 

S. Kaliszewski, Magnus B. Landstad, and John Quigg
Exotic group C*algebras in noncommutative duality view print


Published: 
October 29, 2013 
Keywords: 
group C*algebra, coaction, C*bialgebra, Hopf C*algebra, quantum group, FourierStieltjes algebra 
Subject: 
Primary 46L05 


Abstract
We
show that for
a locally compact group G
there is a onetoone correspondence between Ginvariant weak*closed subspaces E of the FourierStieltjes algebra B(G) containing B_{r}(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 "Ecrossed products'' B\rtimes_{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 crossedproduct duality involving C*_{E}(G).


Author information
S. Kaliszewski:
School of Mathematical and Statistical Sciences, Arizona State University, Tempe, Arizona 85287
kaliszewski@asu.edu
Magnus B. Landstad:
Department of Mathematical Sciences, Norwegian University of Science and Technology, NO7491 Trondheim, Norway
magnusla@math.ntnu.no
John Quigg:
School of Mathematical and Statistical Sciences, Arizona State University, Tempe, Arizona 85287
quigg@asu.edu

