D'Andrea, Francesco
[UCL]
Dabrowski, Ludwik
Landi, Giovanni
(eng)
We study the spectral geometry of the quantum projective plane CP^2_q, a
deformation of the complex projective plane CP^2, the simplest example of a
spin^c manifold which is not spin. In particular, we construct a Dirac operator
D which gives a 0^+ summable spectral triple, equivariant under U_q(su(3)). The
square of D is a central element for which left and right actions on spinors
coincide, a fact that is exploited to compute explicitly its spectrum.
Comment: v2: 26 pages. Paper completely reorganized; no major change, several
minor ones
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Bibliographic reference |
D'Andrea, Francesco ; Dabrowski, Ludwik ; Landi, Giovanni. The Noncommutative Geometry of the Quantum Projective Plane. In: Reviews in Mathematical Physics : a journal for survey and expository articles in the field of mathematical physics, Vol. 20, no. 8, p. 979-1006 (2008) |
Permanent URL |
http://hdl.handle.net/2078/31104 |