Extending lazy 2-cocycles on Hopf algebras and lifting projective representations afforded by them

We study some problems related to lazy 2-cocycles, such as: extension of (lazy) 2-cocycles to a Drinfeld double and to a Radford biproduct, Yetter–Drinfeld data obtained from lazy 2-cocycles, lifting of projective representations afforded by lazy 2-cocycles.