On the presentation of pointed Hopf algebras
Michael Helbig

TL;DR
This paper provides a generator-and-relations presentation for a class of pointed Hopf algebras, including generalized quantum groups and Nichols algebras, enhancing their structural understanding and classification.
Contribution
It introduces a new presentation framework for pointed Hopf algebras generated by skew-primitive elements and abelian group-like elements, extending the understanding of their structure.
Findings
Provides a presentation for pointed Hopf algebras with skew-primitive generators
Derives an analog presentation for Nichols algebras of diagonal type
Enhances classification methods for quantum groups and related structures
Abstract
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.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Nonlinear Waves and Solitons · Advanced Topics in Algebra
