Dilations of partial representations of Hopf algebras

Abstract

We introduce the notion of a dilation for a partial representation (i.e. a partial module) of a Hopf algebra, which in case the partial representation origins from a partial action (i.e.a partial module algebra) coincides with the enveloping action (or globalization). This construction leads to categorical equivalences between the category of partial $H$-modules, a category of (global) $H$-modules endowed with a projection satisfying a suitable commutation relation and the category of modules over a (global) smash product constructed upon $H$, from which we deduce the structure of a Hopfish algebra on this smash product. These equivalences are used to study the interactions between partial and global representation theory.

25 pages. Corrected several typos, final version to appear in Journal of the London Mathematical Society

References in corpus (2)

• Duality for partial group actions
• Globalization of Twisted partial Hopf actions

Cited by in corpus (7)

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• Partial and global representations of finite groups
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• Geometrically Partial actions
• Partial monoid actions on objects in categories with pullbacks and their globalizations