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Fuzzy Complex Grassmannian Spaces and their Star Products

Dolan, Brian P. and Jahn, Oliver (2003) Fuzzy Complex Grassmannian Spaces and their Star Products. International Journal of Modern Physics A, 18 (11). pp. 1935-1957.

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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.

Item Type: Article
Keywords: differential geometry, matrix algebras, fuzzy spaces
Academic Unit: Faculty of Science and Engineering > Experimental Physics
Item ID: 258
Depositing User: Dr. Brian Dolan
Date Deposited: 07 Oct 2005
Journal or Publication Title: International Journal of Modern Physics A
Publisher: World Scientific
Refereed: Yes

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