Galois corings and groupoids acting partially on algebras

Stefaan Caenepeel, Timmy Fieremans

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Samenvatting

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.
Originele taal-2English
Artikelnummer2140003
Aantal pagina's19
TijdschriftJournal of Algebra and Its Applications
Volume20
Nummer van het tijdschrift1
DOI's
StatusPublished - jan 2021

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