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Fuzzy complex projective spaces and their star-products

✍ Scribed by A.P. Balachandran; Brian P. Dolan; J. Lee; X. Martin; Denjoe O’Connor

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
177 KB
Volume
43
Category
Article
ISSN
0393-0440

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✦ Synopsis

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

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