TY  - JOUR
AB  - We extend the construction of generalized fixed point algebras to the setting of locally compact quantum groups – in the sense of Kustermans and Vaes – following the treatment of Marc Rieffel, Ruy Exel and Ralf Meyer in the group case. We mainly follow Meyer’s approach analyzing the constructions in the realm of equivariant Hilbert modules. We generalize the notion of continuous square-integrability, which is exactly what one needs in order to define generalized fixed point algebras. As in the group case, we prove that there is a correspondence between continuously square-integrable Hilbert modules over an equivariant C*-algebra B and Hilbert modules over the reduced crossed product of B by the underlying quantum group. The generalized fixed point algebra always appears as the algebra of compact operators of the associated Hilbert module over the reduced crossed product.
AU  - Buss, Alcides
DA  - 2013
LA  - eng
IS  - Münster Journal of Mathematics
M2  - 295
PY  - 2013
SP  - 295-341
T2  - Münster Journal of Mathematics
TI  - Generalized fixed point algebras for coactions of locally compact quantum groups
UR  - https://nbn-resolving.org/urn:nbn:de:hbz:6-55309458340
Y2  - 2024-11-22T05:39:31
ER  -