Multiplication Alteration by Two-Cocycles: The Non-associative Version

In this paper, we introduce the theory of multiplication alteration by two-cocycles for non-associative structures like non-associative bimonoids with left (right) division. Also, we explore the connections between Yetter–Drinfeld modules for Hopf quasigroups, projections of Hopf quasigroups, skew p...

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Bibliographic Details
Published in:Bulletin of the Malaysian Mathematical Sciences Society 2020-09, Vol.43 (5), p.3557-3615
Main Authors: Álvarez, J. N. Alonso, Vilaboa, J. M. Fernández, Rodríguez, R. González
Format: Article
Language:English
Subjects:
Applications of Mathematics
Mathematics
Mathematics and Statistics
Multiplication
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Summary:In this paper, we introduce the theory of multiplication alteration by two-cocycles for non-associative structures like non-associative bimonoids with left (right) division. Also, we explore the connections between Yetter–Drinfeld modules for Hopf quasigroups, projections of Hopf quasigroups, skew pairings and quasitriangular structures, obtaining the non-associative version of the main results proved by Doi and Takeuchi in the Hopf algebra setting.
ISSN:0126-6705
2180-4206
DOI:10.1007/s40840-019-00885-8