English

On the lifting of Nichols algebras

Quantum Algebra 2010-03-31 v1

Abstract

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.

Keywords

Cite

@article{arxiv.1003.5882,
  title  = {On the lifting of Nichols algebras},
  author = {Michael Helbig},
  journal= {arXiv preprint arXiv:1003.5882},
  year   = {2010}
}