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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
Subjects: Science & 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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