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Galois corings and groupoids acting partially on algebras

Journal Contribution - Journal Article

Bagio and Paques [Partial groupoid actions: globalization, Morita theory and Galois theory, Comm. Algebra 40 (2012) 3658–3678] developed a Galois theory for unital partial actions by finite groupoids. The aim of this note is to show that this is actually a special case of the Galois theory for corings, as introduced by Brzezin ́ski [The structure of corings, Induction functors, Maschke-type theorem, and Frobenius and Galois properties, Algebr. Represent. Theory 5 (2002) 389–410]. To this end, we associate a coring to a unital partial action of a finite groupoid on an algebra A, and show that this coring is Galois if and only if A is an α-partial Galois extension of its coinvariants.
Journal: Journal of Algebra & Its Applications
ISSN: 0219-4988
Issue: 1
Volume: 20
Publication year:2021
Keywords:Galois coring, partial action, groupoid
BOF-keylabel:yes
IOF-keylabel:yes
BOF-publication weight:0.5
Authors:Regional
Authors from:Higher Education
Accessibility:Closed