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Fuzzy Complex Projective Spaces and their Star-products

Balachandran, A.P. and Dolan, Brian P. and Lee, J. and Martin, X. and O'Connor, Denjoe (2002) Fuzzy Complex Projective Spaces and their Star-products. Journal of Geometry and Physics , 43 (2/3). pp. 184-204. ISSN 0393-0440

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Abstract

We derive an explicit expression for an associative ∗-product on the fuzzy complex projective space, CPN−1 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.

Item Type: Article
Additional Information: 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.
Keywords: Fuzzy Complex Projective Space; Star-Product; Non-commutative geometry;
Subjects: Science & Engineering > Mathematical Physics
Item ID: 2716
Identification Number: 10.1016/S0393-0440(02)00020-7
Depositing User: Dr. Brian Dolan
Date Deposited: 15 Sep 2011 10:45
Journal or Publication Title: Journal of Geometry and Physics
Publisher: Elsevier
Refereed: No
URI:

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