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Classifying partial (co)actions of Taft and Nichols Hopf algebras on their base fields
Graziela Fonseca, Grasiela Martini, Leonardo Silva
In this paper we determine all partial actions and partial coactions of Taft and Nichols Hopf algebras on their base fields. Furthermore, we prove that all such partial (co)actions…
Partial Actions of a Hopf algebra on its base field and the corresponding partial smash product algebra
Grasiela Martini, Antonio Paques, Leonardo Duarte Silva
We introduce the concept of a -Hopf algebra as a Hopf algebra obtained as the partial smash product algebra of a Hopf algebra and its base field, and show that every Hopf algebr…
Examples of Nichols algebras associated to upper triangular solutions of the Yang-Baxter equation in rank 3
João Matheus Jury Giraldi, Leonardo Duarte Silva
We determine some Nichols algebras that admit a non-trivial quadratic relation associated to some families of upper triangular solutions of the Yang-Baxter equation of dimension 3.