Operator Algebra Quantum Homogeneous Spaces of Universal Gauge Groups
Abstract
In this paper, we quantize universal gauge groups such as SU(∞), as well as their homogeneous spaces, in the σ C*algebra setting. More precisely, we propose concise definitions of σ C*quantum groups and σ C*quantum homogeneous spaces and explain these concepts here. At the same time, we put these definitions in the mathematical context of countably compactly generated spaces as well as C*compact quantum groups and homogeneous spaces. We also study the representable Ktheory of these spaces and compute these groups for the quantum homogeneous spaces associated to the quantum version of the universal gauge group SU(∞).
 Publication:

Letters in Mathematical Physics
 Pub Date:
 September 2011
 DOI:
 10.1007/s110050110492y
 arXiv:
 arXiv:1012.5893
 Bibcode:
 2011LMaPh..97..263M
 Keywords:

 Mathematics  Quantum Algebra;
 High Energy Physics  Theory;
 Mathematics  KTheory and Homology;
 Mathematics  Operator Algebras;
 46L80;
 58B32;
 58B34;
 46L65
 EPrint:
 14 pages. Merged with [arXiv:1011.1073]