Modular Images Of Approximately Central Projections
Samuel G. Walters

TL;DR
This paper classifies approximately central projections in the Flip orbifold of an irrational rotation algebra under modular automorphisms, showing their equivalence classes form an orbit under certain transformations and linking automorphisms via K-theory.
Contribution
It provides a detailed classification of AC projections under modular automorphisms in the Flip orbifold, extending understanding of their equivalence and automorphism actions.
Findings
AC projections are classified up to Murray-von Neumann equivalence within an orbit of transformations.
Automorphisms with the same K_0 action produce centrally equivalent projections.
The classification involves Fourier and Cubic transforms forming an S_3-orbit.
Abstract
It is shown that for any approximately central (AC) projection in the Flip orbifold (of the irrational rotation C*-algebra ), and any modular automorphism (arising from SL), the AC projection is centrally Murray-von Neumann equivalent to one of the projections in the -orbit of where are the Fourier and Cubic transforms of . (The equivalence being implemented by an approximately central partial isometry in .) For smooth automorphisms of the Flip orbifold , it is also shown that if on then and are centrally equivalent for each AC projection .
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
TopicsAdvanced Operator Algebra Research · Advanced Topics in Algebra · Advanced Algebra and Geometry
