slides

Functorial Cocycle Deformation
Now we pass to noncommutative geometry. We view the deformation as a functor
LF : H C → HF C
from a certain category H C (wherein lives our classical geometry) to a new
category HF C, both to be determined.
Let H be a commutative unital Hopf algebra. Let F : H ⊗ H → C be a
convolution-invertible unital two-cocycle on H.
Then there is a new Hopf algebra HF which is the same as H as a coalgebra,
but has the new product
h •F g := F (h (1), g (1))h (2)g (2)F −1 (h (3), g (3)).
S. Brain (RU) NCG of Self-Dual Gauge Fields Nijmegen, 12th October 2010 11 / 25