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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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.

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
URI:	http://arxiv.org/abs/hep-th/0111020
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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