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arXiv · hep-th/0111020

Fuzzy Complex Grassmannian Spaces and their Star Products

Brian P. Dolan·Oliver Jahn
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Abstract

We derive an explicit expression for an associative star product on non-commutative versions of complex Grassmannian spaces, in particular for the case of complex 2-planes. Our expression is in terms of a finite sum of derivatives. This generalises previous results for complex projective spaces and gives a discrete approximation for the Grassmannians in terms of a non-commutative algebra, represented by matrix multiplication in a finite-dimensional matrix algebra. The matrices are restricted to have a dimension which is precisely determined by the harmonic expansion of functions on the commutative Grassmannian, truncated at a finite level. In the limit of infinite-dimensional matrices we recover the commutative algebra of functions on the complex Grassmannians.

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Brian P. Dolan, Oliver Jahn. 2003-01-07. Fuzzy Complex Grassmannian Spaces and their Star Products. https://doi.org/10.1142/s0217751x03014113

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