Classifying coalgebra split extensions of Hopf algebras
A. L. Agore, C. G. Bontea, G. Militaru

TL;DR
This paper classifies all coalgebra split extensions of a Hopf algebra by the Sweedler's 4-dimensional Hopf algebra, explicitly describing the crossed products and their automorphisms, including new examples in characteristic p.
Contribution
It provides a complete classification of coalgebra split extensions of Hopf algebras by H_4, including explicit generators, relations, and automorphism groups, with new examples in characteristic p.
Findings
Classified all Hopf algebra extensions by H_4.
Explicitly described crossed products via generators and relations.
Constructed infinite families of non-isomorphic Hopf algebras in characteristic p.
Abstract
For a given Hopf algebra we classify all Hopf algebras that are coalgebra split extensions of by , where is the Sweedler's 4-dimensional Hopf algebra. Equivalently, we classify all crossed products of Hopf algebras A # H_4 by computing explicitly two classifying objects: the cohomological 'group' and the set of types of isomorphisms of all crossed products A # H_4. All crossed products A #H_4 are described by generators and relations and classified: they are parameterized by the set of all central primitive elements of . Several examples are worked out in detail: in particular, over a field of characteristic an infinite family of non-isomorphic Hopf algebras of dimension is constructed. The groups of automorphisms of these Hopf algebras…
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Nonlinear Waves and Solitons
