Geometrically partial actions
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- by Jiawei Hu and Joost Vercruysse PDF
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Abstract:
We introduce “geometric” partial comodules over coalgebras in monoidal categories as an alternative notion to the notion of partial action and coaction of a Hopf algebra introduced by Caenepeel and Janssen. The name is motivated by the fact that our new notion suits better if one wants to describe phenomena of partial actions in algebraic geometry. Under mild conditions, the category of geometric partial comodules is shown to be complete and cocomplete and the category of partial comodules over a Hopf algebra is lax monoidal. We develop a Hopf-Galois theory for geometric partial coactions to illustrate that our new notion might be a useful additional tool in Hopf algebra theory.References
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Additional Information
- Jiawei Hu
- Affiliation: Department of Mathematical Sciences, East China Normal University, No. 500, Dongchuan Road, Shanghai, People’s Republic of China; and Département de Mathématiques, Faculté des sciences, Université Libre de Bruxelles, Boulevard du Triomphe, B-1050 Bruxelles, Belgium
- Email: hhjjwilliam@gmail.com, ohujiaweio@163.com
- Joost Vercruysse
- Affiliation: Département de Mathématiques, Faculté des sciences, Université Libre de Bruxelles, Boulevard du Triomphe, B-1050 Bruxelles, Belgium
- MR Author ID: 734258
- ORCID: 0000-0002-8154-5357
- Email: jvercruy@ulb.ac.be
- Received by editor(s): May 27, 2018
- Received by editor(s) in revised form: July 9, 2019, September 9, 2019, and September 11, 2019
- Published electronically: March 10, 2020
- Additional Notes: Jiawei Hu is the corresponding author
- © Copyright 2020 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 373 (2020), 4085-4143
- MSC (2010): Primary 14R20, 18D10, 16T05
- DOI: https://doi.org/10.1090/tran/8058
- MathSciNet review: 4105519