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Fuzzy complex projective spaces and their star-products

2002; Elsevier BV; Volume: 43; Issue: 2-3 Linguagem: Inglês

10.1016/s0393-0440(02)00020-7

1879-1662

A. P. Balachandran, Brian P. Dolan, J. Lee, Xavier Martín, Denjoe O’Connor,

Algebraic structures and combinatorial models

We derive an explicit expression for an associative ∗-product on the fuzzy complex projective space, CPN−1F. This generalises previous results for the fuzzy 2-sphere and gives a discrete non-commutative algebra of functions on CPN−1F, 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−1F are also expressed as matrix commutators.