Twisted Dirac operator on quantum SU(2) in disc coordinates
Ulrich Kraehmer, Elmar Wagner
TL;DR
This paper constructs twisted Dirac operators on quantum SU(2) using the quantum disc as a coordinate chart, revealing their gauge relationship and bounded commutators with differentiable functions.
Contribution
It introduces two related twisted Dirac operators on quantum SU(2) derived from the quantum disc, expanding the noncommutative geometric framework.
Findings
The two Dirac operators are related by a gauge transformation.
Both operators have bounded twisted commutators with a suitable algebra.
The quantum disc serves as a noncommutative coordinate chart for quantum SU(2).
Abstract
The quantum disc is used to define a noncommutative analogue of a dense coordinate chart and of left-invariant vector fields on quantum SU(2). This yields two twisted Dirac operators for different twists that are related by a gauge transformation and have bounded twisted commutators with a suitable algebra of differentiable functions on quantum SU(2).
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsNoncommutative and Quantum Gravity Theories · Advanced Operator Algebra Research · Advanced Topics in Algebra