Balachandran, A.P. and Dolan, Brian P. and Lee, J. and Martin, X. and O'Connor, Denjoe
Fuzzy Complex Projective Spaces and their Star-products.
Journal of Geometry and Physics , 43 (2/3).
We derive an explicit expression for an associative ∗-product on the fuzzy complex projective
F . This generalises previous results for the fuzzy 2-sphere and gives
a discrete non-commutative algebra of functions on CPN−1
F , represented by matrix multiplication.
The matrices are restricted to ones whose dimension is that of the totally
symmetric representations of SU(N). In the limit of infinite dimensional matrices we recover
the commutative algebra of functions on CPN−1. Derivatives on CPN−1
F are also
expressed as matrix commutators.
||Preprint version of published article. It is a pleasure to thank Oliver Jahn for discussions, and in particular for pointing out
the identity (6.13) to us, and Peter Preˇsnajder for useful comments. We have benefited
greatly from participating in the study groups at CINVESTAV, Mexico D.F. and Syracuse
during the Summer and Fall of 2000, and the Summer of 2001. This work was supported
by DOE contract DE-FG02-85ERR40231, NSF grant INT-9908763, joint NSF-CONACyT
grant E120.0462/2000, CONACyT grant 30422-E and Enterprise Ireland, Basic Research
grant SC/1998/739. B.D. would also like to thank the Dublin Institute for Advanced
Studies for financial support.
||Fuzzy Complex Projective Space; Star-Product; Non-commutative geometry;
||Science & Engineering > Mathematical Physics
Dr. Brian Dolan
||15 Sep 2011 10:45
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