Fuzzy Complex Projective Spaces and their Star-products

Details Fuzzy Complex Projective Spaces and their Star-products Fuzzy Complex Projective Spaces and their Star-products

2001-07-12

arxiv.org/abs/hep-th/0107099v2

J.Geom.Phys. 43 (2002) 184-204

Physics

High Energy Physics

High Energy Physics - Theory

20 pages, typeset in plain TeX

Scientific paper

10.1016/S0393-0440(02)00020-7

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

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