A Characterization of Weak Hopf (co) Quasigroups

In this paper, we show that weak Hopf (co)quasigroups can be characterized by a Galois-type condition. Taking into account that this notion generalizes the ones of Hopf (co)quasigroup and weak Hopf algebra, we obtain as a consequence the first fundamental theorem for Hopf (co)quasigroups and a chara...

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Bibliographic Details
Published in:Mediterranean journal of mathematics 2016-10, Vol.13 (5), p.3747-3764
Main Authors: Alonso Álvarez, J. N., Fernández Vilaboa, J. M., González Rodríguez, R.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary:In this paper, we show that weak Hopf (co)quasigroups can be characterized by a Galois-type condition. Taking into account that this notion generalizes the ones of Hopf (co)quasigroup and weak Hopf algebra, we obtain as a consequence the first fundamental theorem for Hopf (co)quasigroups and a characterization of weak Hopf algebras in terms of bijectivity of a Galois-type morphism (also called fusion morphism).
ISSN:1660-5446
1660-5454
DOI:10.1007/s00009-016-0712-x