Quantum group connections
Mathematical Physics
2010-11-02 v2 General Relativity and Quantum Cosmology
High Energy Physics - Theory
math.MP
Abstract
The Ahtekar-Isham C*-algebra known from Loop Quantum Gravity is the algebra of continuous functions on the space of (generalized) connections with a compact structure Lie group. The algebra can be constructed by some inductive techniques from the C*-algebra of continuous functions on the group and a family of graphs embedded in the manifold underlying the connections. We generalize the latter construction replacing the commutative C*-algebra of continuous functions on the group by a non-commutative C*-algebra defining a compact quantum group.
Cite
@article{arxiv.0810.2992,
title = {Quantum group connections},
author = {Jerzy Lewandowski and Andrzej Okolow},
journal= {arXiv preprint arXiv:0810.2992},
year = {2010}
}
Comments
40 pages, LaTeX2e, minor mistakes corrected, abstract slightly changed