Partial Representations of Hopf Algebras

Marcelo Muniz S. Alves; Eliezer Batista; Joost Vercruysse

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arXiv · 1309.1659

Partial Representations of Hopf Algebras

Marcelo Muniz S. Alves·Eliezer Batista·Joost Vercruysse

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Abstract

In this work, the notion of partial representation of a Hopf algebra is introduced and its relationship with partial actions of Hopf algebras is explored. Given a Hopf algebra $H$, one can associate it to a Hopf algebroid $H_{par}$ which has the universal property that each partial representation of $H$ can be factorized by an algebra morphism from $H_{par}$. We define also the category of partial modules over a Hopf algebra $H$, which is the category of modules over its associated Hopf algebroid $H_{par}$. The Hopf algebroid structure of $H_{par}$ enables us to enhance the category of partial $H$ modules with a monoidal structure and such that the algebra objects in this category are the usual partial actions. Some examples of categories of partial $H$ modules are explored. In particular we can describe fully the category of partially $\mathbb{Z}_2$-graded modules.

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BibTeX RIS

Marcelo Muniz S. Alves, Eliezer Batista, Joost Vercruysse. 2013-09-20. Partial Representations of Hopf Algebras. https://arxiv.org/abs/1309.1659

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