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J. Korean Math. Soc. 2017; 54(2): 517-543

Online first article December 7, 2016      Printed March 1, 2017

https://doi.org/10.4134/JKMS.j160118

Copyright © The Korean Mathematical Society.

The group of strong Galois objects associated to a cocommutative Hopf quasigroup

Jose N. Alonso \'Alvarez, Ramon Gonz\'{a}lez Rodr\'iguez, and Jose M. Fern\'andez Vilaboa

Universidad de Vigo, E.T.S.I. Telecomunicaci\'on Universidad de Vigo, Universidad de Santiago de Compostela

Abstract

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Let $H$ be a cocommutative faithfully flat Hopf quasigroup in a strict symmetricmonoidal category with equalizers. In this paper we introduce the notion of (strong) Galois $H$-object and we prove that the set of isomorphism classes of (strong) Galois $H$-objects is a (group) monoid which coincides, in the Hopf algebra setting, with the Galois group of $H$-Galois objects introduced by Chase and Sweedler.

Keywords: monoidal category, unital magma, Hopf quasigroup, (strong) Galois $H$-object, Galois group, normal basis

MSC numbers: 18D10, 17A01, 16T05, 81R50, 20N05

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