A PBW basis criterion for pointed Hopf algebras

Details A PBW basis criterion for pointed Hopf algebras A PBW basis criterion for pointed Hopf algebras

2010-10-31

arxiv.org/abs/1011.0140v1

Mathematics

Quantum Algebra

29 pages

Scientific paper

We give a necessary and sufficient PBW basis criterion for Hopf algebras generated by skew-primitive elements and abelian group of group-like elements with action given via characters. This class of pointed Hopf algebras has shown great importance in the classification theory and can be seen as generalized quantum groups. We apply the criterion to classical examples and liftings of Nichols algebras which were determined in arxiv.org:1003.5882.

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