Fuzzy Complex Projective Spaces and their Star-products
High Energy Physics - Theory
2009-11-07 v2 General Relativity and Quantum Cosmology
Quantum Algebra
Abstract
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.
Cite
@article{arxiv.hep-th/0107099,
title = {Fuzzy Complex Projective Spaces and their Star-products},
author = {A. P. Balachandran and Brian P. Dolan and J. Lee and X. Martin and Denjoe O'Connor},
journal= {arXiv preprint arXiv:hep-th/0107099},
year = {2009}
}
Comments
20 pages, typeset in plain TeX