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Keywords = multiplier Hopf coquasigroup

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19 pages, 294 KB  
Article
Ore Extensions of Multiplier Hopf Coquasigroups
by Rui Zhang, Na Zhang, Yapeng Zeng and Tao Yang
Axioms 2025, 14(11), 778; https://doi.org/10.3390/axioms14110778 - 23 Oct 2025
Viewed by 958
Abstract
This paper introduces and investigates Ore extensions in the context of multiplier Hopf coquasigroups, a structure that generalizes both multiplier Hopf algebras and Hopf coquasigroups. We establish necessary and sufficient conditions under which an Ore extension of a regular multiplier Hopf coquasigroup itself [...] Read more.
This paper introduces and investigates Ore extensions in the context of multiplier Hopf coquasigroups, a structure that generalizes both multiplier Hopf algebras and Hopf coquasigroups. We establish necessary and sufficient conditions under which an Ore extension of a regular multiplier Hopf coquasigroup itself forms a regular multiplier Hopf coquasigroup. Furthermore, we explore the isomorphism problem for such Ore extensions, providing criteria for the equivalence of two extensions. The case of multiplier Hopf coquasigroups is also analyzed, with conditions derived for the Ore extension to inherit the structure. Our results unify and extend prior work on Ore extensions in the settings of Hopf algebras, multiplier Hopf algebras, and Hopf coquasigroups. Full article
(This article belongs to the Special Issue Advances in Hopf Algebras, Tensor Categories and Related Topics)
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23 pages, 317 KB  
Article
Multiplier Hopf Coquasigroup: Motivation and Biduality
by Tao Yang
Mathematics 2022, 10(21), 4006; https://doi.org/10.3390/math10214006 - 28 Oct 2022
Cited by 2 | Viewed by 1729
Abstract
Inspired by the multiplier Hopf algebra theory introduced by A. Van Daele, this paper introduces a new algebraic structure, a multiplier Hopf coquasigroup, by constructing the integral dual of an infinite-dimensional Hopf quasigroup with faithful integrals. Then, it shows that the biduality theorem [...] Read more.
Inspired by the multiplier Hopf algebra theory introduced by A. Van Daele, this paper introduces a new algebraic structure, a multiplier Hopf coquasigroup, by constructing the integral dual of an infinite-dimensional Hopf quasigroup with faithful integrals. Then, it shows that the biduality theorem also holds for Hopf quasigroups and multiplier Hopf coquasigroups of the discrete type. Full article
(This article belongs to the Special Issue New Advances in Algebra, Ring Theory and Homological Algebra)
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