Lifting of Nichols Algebras of Type $B_2$, with an Appendix: A generalization of the q-binomial theorem

Details Lifting of Nichols Algebras of Type $B_2$, with an Appendix: A generalization of the q-binomial theorem Lifting of Nichols Algebras of Type $B_2$, with an Appendix: A generalization of the q-binomial theorem

2002-04-05

arxiv.org/abs/math/0204075v1

Mathematics

Quantum Algebra

25 pages. Appendix with Ian Rutherford

Scientific paper

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 $n$th roots of 1 with odd $n\neq 5$. As well, we compute the liftings 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.

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