  Nichols algebras are a fundamental building block of pointed Hopf algebras.
Part of the classification program of finite-dimensional pointed Hopf algebras
with the lifting method of Andruskiewitsch and Schneider is the determination
of the liftings, i.e., all possible deformations of a given Nichols algebra.
Based on recent work of Heckenberger about Nichols algebras of diagonal type we
compute explicitly the liftings of all Nichols algebras with Cartan matrix of
type A_2, some Nichols algebras with Cartan matrix of type B_2, and some
Nichols algebras of two Weyl equivalence classes of non-standard type, giving
new classes of finite-dimensional pointed Hopf algebras.
