On the lifting of Nichols algebras

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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 A₂, some Nichols algebras with Cartan matrix of type B₂, and some Nichols algebras of two Weyl equivalence classes of non-standard type, giving new classes of finite-dimensional pointed Hopf algebras.