Fuzzy complex projective spaces and their star-products

[摘要] We derive an explicit expression for an associative (*)-product on the fuzzy complex projective space, CPFN-1. This generalises previous results for the fuzzy 2-sphere and gives a discrete non-commutative algebra of functions on CPFN-1, 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 CPFN-1 are also expressed as matrix commutators. (C) 2002 Elsevier Science B.V. All rights reserved.

[发布日期] 2002-09-01

[关键词] non-commutative geometry;star-product