TY  - INPR
U1  - Preprint
A1  - Helbig, Michael
T1  - A PBW basis criterion for pointed Hopf algebras
N2  - 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.
AB  - 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.
KW  - Quantum Algebra
KW  - Hopf algebra
KW  - Nichols algebra
Y1  - 2025
U6  - https://doi.org/10.48550/arxiv.1011.0140
DO  - https://doi.org/10.48550/arxiv.1011.0140
SP  - 1
EP  - 33
S1  - 33
ER  -