Dolan, Brian P. and Jahn, Oliver
(2003)
Fuzzy Complex Grassmannian Spaces and their Star Products.
International Journal of Modern Physics A, 18 (11).
pp. 19351957.
Abstract
We derive an explicit expression for an associative star product on noncommutative versions of complex Grassmannian spaces, in particular for the case of complex 2planes. 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 noncommutative algebra, represented by matrix multiplication in a finitedimensional 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 infinitedimensional 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 
URI: 

Repository Staff Only(login required)

Item control page 