Dilations of partial representations of Hopf algebras
We introduce the notion of a dilation for a partial representation (that is, a partial module) of a Hopf algebra, which in case the partial representation origins from a partial action (that is, a partial module algebra) coincides with the enveloping action (or globalization). This construction lead...
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| Published in: | Journal of the London Mathematical Society Vol. 100; no. 1; pp. 273 - 300 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
01-08-2019
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| Subjects: | |
| Online Access: | Get full text |
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| Summary: | We introduce the notion of a dilation for a partial representation (that is, a partial module) of a Hopf algebra, which in case the partial representation origins from a partial action (that is, 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. |
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| Bibliography: | The first author is partially supported by CNPq, grant number 306583/2016‐0. The third author would like to thank the FWB (Fédération Wallonie‐Bruxelles) for financial support via the ARC‐project ‘Hopf algebras and the symmetries of non‐commutative spaces’ as well as the FNRS for the MIS‐project ‘Antipode’. All authors thank the anonymous referee for his/her useful comments that improved the presentation of this paper. |
| ISSN: | 0024-6107 1469-7750 |
| DOI: | 10.1112/jlms.12213 |