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 noncommutative C*-algebra defining a compact quantum group.