Quantum group connections

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.

40 pages, LaTeX2e, minor mistakes corrected, abstract slightly changed

References in corpus (2)

• Uniqueness of diffeomorphism invariant states on holonomy-flux algebras
• Spectral triples of holonomy loops

Cited by in corpus (3)

• Non-commutative flux representation for loop quantum gravity
• Observables in Loop Quantum Gravity with a cosmological constant
• Local Observables in ${\mathrm{SU}}_q(2)$ Lattice Gauge Theory