3151 2010 eng 1 13 13 preprint 0 -- 2025-12-18 -- We give a presentation in terms of generators and relations of 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. As a consequence we get an analog presentation of Nichols algebras of diagonal type. 10.48550/arXiv.1003.5879 Nein publish false false 2 Michael Helbig eng uncontrolled Quantum Algebra eng uncontrolled Hopf algebra eng uncontrolled Nichols algebra Mathematik Fakultät für Angewandte Natur- und Geisteswissenschaften Technische Hochschule Rosenheim