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Addenda to “Correspondence theorems for Hopf algebroids with applications to affine groupoids”

Part of: Special categories Hopf algebras, quantum groups and related topics

Published online by Cambridge University Press:  27 December 2024

Laiachi El Kaoutit ,
Aryan Ghobadi ,
Paolo Saracco Open the ORCID record for Paolo Saracco [Opens in a new window]  and
Joost Vercruysse Open the ORCID record for Joost Vercruysse [Opens in a new window]
Laiachi El Kaoutit
Affiliation:
Universidad de Granada, Departamento de Álgebra and IMAG. Facultad de Ciencias, Fuente Nueva s/n. E810071 Granada, Spain e-mail: kaoutit@ugr.es URL: http://www.ugr.es/~kaoutit/
Aryan Ghobadi
Affiliation:
Département de Mathématique, Université Libre de Bruxelles, Boulevard du Triomphe, B-1050 Brussels, Belgium URL: https://sites.google.com/view/paolo-saracco URL: https://paolo.saracco.web.ulb.be
Paolo Saracco*
Affiliation:
Département de Mathématique, Université Libre de Bruxelles, Boulevard du Triomphe, B-1050 Brussels, Belgium URL: https://sites.google.com/view/paolo-saracco URL: https://paolo.saracco.web.ulb.be
Joost Vercruysse
Affiliation:
Département de Mathématique, Université Libre de Bruxelles, Boulevard du Triomphe, B-1050 Brussels, Belgium e-mail: joost.vercruysse@ulb.be URL: http://joost.vercruysse.web.ulb.be
*
e-mail: paolo.saracco@ulb.be
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Abstract

The proof of Theorem 3.14 contains an unsubstantiated claim. To overcome this problem, we add a hypothesis to the statement of 3.14 and we provide a new valid proof. We adjust Theorem 3.15, Corollary 3.16, Proposition 4.23, Theorem 4.26, Corollary 4.29, and Corollary 4.32 accordingly.

Keywords

Hopf algebroidsnormal idealsaffine groupoids normal affine subgroupoidscomodule algebrasfinite groupoidsHopf algebroids of functionsGalois correspondence

MSC classification

Primary: 16T05: Hopf algebras and their applications 16T15: Coalgebras and comodules; corings 18B40: Groupoids, semigroupoids, semigroups, groups (viewed as categories)
Type
Addendum
Information
Canadian Journal of Mathematics , First View , pp. 1 - 4
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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References

Ghobadi, A., El Kaoutit, L., Saracco, P., and Vercruysse, J., Correspondence theorems for Hopf algebroids with applications to affine groupoids . Canad. J. Math. 76(2024), no. 3, 830–880.Google Scholar
Saracco, P., A remark on the Galois-type correspondence between ideal coideals and comodule subrings of a Hopf algebroid . Bull. Belg. Math. Soc. Simon Stevin 30(2023), no. 5, 668–682.CrossRefGoogle Scholar