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arXiv · 2009.08540

Partial Actions of a Hopf algebra on its base field and the corresponding partial smash product algebra

Grasiela Martini·Antonio Paques·Leonardo Duarte Silva
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Abstract

We introduce the concept of a $λ$-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 algebra is a $λ$-Hopf algebra. Moreover, a method to compute partial actions of a given Hopf algebra on its base field is developed and, as an application, we exhibit all partial actions of such type for some families of Hopf algebras.

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Grasiela Martini, Antonio Paques, Leonardo Duarte Silva. 2022-02-21. Partial Actions of a Hopf algebra on its base field and the corresponding partial smash product algebra. https://arxiv.org/abs/2009.08540

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