uniform continuity over locally compact quantum groupoids
0.1 Uniform Continuity over Locally Compact Quantum Groupoids
Let us consider Locally Compact Quantum Groupoids () defined as locally compact groupoids endowed with a Haar system, , , or as derived from a (non-commutative) weak Hopf algebra (WHA), with the additional condition of uniform continuity over defined as follows . Let us also consider a space of left uniformly continuous elements in defined over , which is endowed with the induced product topology from the subset of composable pairs in the topological groupoid . This step completes the construction of uniform continuity over that can be then compared with the results obtained from ‘quantum groupoids’ derived from a weak Hopf algebra.
0.1.1 C*-algebra Comparison and Example
Consider to be a locally compact quantum group. Then consider the space of left uniformly continuous elements in introduced in ref. . (The definition according to V. Runde (loc. cit.) covers both the space of left uniformly continuous functions on a locally compact group and (Granirer’s) uniformly continuous functionals on the Fourier algebra.) Also consider which is then an operator system containing the C*-algebra . One may compare the groupoid C*-convolution algebra, – obtained in the general case– with the C*-algebra (http://planetmath.org/CAlgebra3) obtained from in the particular case of uniform continuity over a locally compact (http://planetmath.org/LocallyCompact) group.
- 1 M. Buneci. 2003. Groupoid Representations, Publs: Ed. Mirton, Timishoara.
- 2 V. Runde. 2008. Uniform continuity over locally compact quantum groups. http://arxiv.org/PS_cache/arxiv/pdf/0802/0802.2053v4.pdf(math.OA -arxiv/0802.2053v4).
|Title||uniform continuity over locally compact quantum groupoids|
|Date of creation||2013-03-22 18:21:21|
|Last modified on||2013-03-22 18:21:21|
|Last modified by||bci1 (20947)|
|Defines||uniform continuity over topological groupoids|