Non-commutative toroidal orbifolds
The above picture shows a foliation of the 2-sphere (with
the slope 1/E). The algebras of foliations of the sphere are related to
C*-algebras of (ir)rational
rotation and their fixed-point subalgebras under the
To find out more about non-commutative orbifolds,
read the link below:
Folowing references contain more detailed information:
- Bratteli, O., Elliott, G.
A., Evans, D. E., and Kishimoto, A.:
Non-commutative spheres, I.
International Journal of Mathematics, 2, 139--166.
- Bratteli, O. and Kishimoto, A.: Non-commutative spheres, III,
Irrational rotations. Communications in Mathematical Physics, 147,
- Bratteli, O., Evans, D. E.
and Kishimoto, A.: Crossed products of
totally disconnected spaces by Z_2 \times Z_2. Ergodic
Theory and Dynamical Systems, 13, 445--484.
- Elliott, G. A. and Evans,
D. E.: The structure of the irrational rotation C*-algebra. Annals
of Mathematics, 138, 477--501.
- Evans, D. E.; Kawahigashi,
Symmetries on Operator Algebras', Oxford University
Below are some more pictures:
All the diagrams have been drawn by Soren
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