As a more nontrivial example for my Dissertation thesis, I'd require some example of the following type (of course I'll "cite" ;-) ), so thanx in advance:
Andruskiewitsch/Grana have by a new construction given very interesting new liftings of finite dimensional Nichols algebras e.g. over $S_4$ ("Examples of liftings of Nichols algebras over racks", 2004).
On the other hand Masuoka has shown, that all the "well-known" liftings of Nichols algebras over abelian groups (finite dimensional, all prime divisors>7, by Andruskiewitsch/Schneider) are Doi/Cocycle-twists of the unlifted/graded one's ("Abelian and non-abelian second cohomologies of quantum enveloping algebras", 2008)
....is there an easy way to see that this is also true for the "new" liftings over nonabelian groups?...and how could I easily read off the precise 2-cocycle?