3 research outputs found
Finitely-Generated Projective Modules over the Theta-deformed 4-sphere
We investigate the "theta-deformed spheres" C(S^{3}_{theta}) and
C(S^{4}_{theta}), where theta is any real number. We show that all
finitely-generated projective modules over C(S^{3}_{theta}) are free, and that
C(S^{4}_{theta}) has the cancellation property. We classify and construct all
finitely-generated projective modules over C(S^{4}_{\theta}) up to isomorphism.
An interesting feature is that if theta is irrational then there are nontrivial
"rank-1" modules over C(S^{4}_{\theta}). In that case, every finitely-generated
projective module over C(S^{4}_{\theta}) is a sum of a rank-1 module and a free
module. If theta is rational, the situation mirrors that for the commutative
case theta=0.Comment: 34 page