Lifting of Nichols algebras of typeB 2

We compute liftings of the Nichols algebra of a Yetter-Drinfeld module of Cartan typeB ₂ subject to the small restriction that the diagnonal elements of the braiding matrix are primitiventh roots of 1 with oddn≠5. As well, we compute the liftings of a Nichols algebra of Cartan typeA 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 typeB ₂ but is also of interest independent of these results. With an appendix “A generalization of theq-binomial theorem” with Ian Rutherford, Department of Mathematics and Computer Science, Mount Allison University, Sackville, N.B., Canada E4L 1E6. Research partially supported by NSERC. A visit to University of Bucharest in 1999 was partially supported by CNCSIS, Grant C12. She would like to thank the department for their warm hospitality. Received partial support from CNCSIS, Grants C12 and 199. Thanks to Mount Allison University for their hospitality in June 1999.