2 00 2 Lifting of Nichols Algebras of Type B 2 ∗

We compute liftings of the Nichols algebra of a Yetter-Drinfeld module of Cartan type B 2 subject to the small restriction that the diagonal elements of the braiding matrix are primitive nth roots of 1 with odd n = 5. As well, we compute the lift-ings of a Nichols algebra of Cartan type A 2 if the diagonal elements of the braiding matrix are cube roots of 1; this case was not completely covered in previous work of Andruskiewitsch and Schneider. We study the problem of when the liftings of a given Nichols algebra are quasi-isomorphic. The Appendix (with I. Rutherford) contains a generalization of the quantum binomial formula. This formula was used in the computation of liftings of type B 2 but is also of interest independent of these results.