locally compact quantum groups: uniform continuity
0.1 Uniform continuity over locally compact quantum groups (LCG)
One can consider locally compact quantum groups () to be defined as a particular case of locally compact quantum groupoids () when the object space of the consists of just one object whose elements are, for example, those of a (non-commutative) Hopf algebra. This is also consistent with the definition introduced by Kustermans and Vaes for a locally compact quantum group by including a Haar measure system associated with the quantum group.
0.2 Operator system containg the C*-algebra
Let us 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.
- 1 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||locally compact quantum groups: uniform continuity|
|Date of creation||2013-03-22 18:21:14|
|Last modified on||2013-03-22 18:21:14|
|Last modified by||bci1 (20947)|
|Synonym||uniform continuity over topological groups associated with Hopf algebras|
|Defines||left uniformly continuous functions on a locally compact group|
|Defines||uniformly continuous functionals on the Fourier algebra|