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 K-theory 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/s11005-011-0492-y
- arXiv:
- arXiv:1012.5893
- Bibcode:
- 2011LMaPh..97..263M
- Keywords:
-
- Mathematics - Quantum Algebra;
- High Energy Physics - Theory;
- Mathematics - K-Theory and Homology;
- Mathematics - Operator Algebras;
- 46L80;
- 58B32;
- 58B34;
- 46L65
- E-Print:
- 14 pages. Merged with [arXiv:1011.1073]