Generalized Hopf–Ore Extensions of Hopf Group-Coalgebras

Ding-Guo Wang and Xing Wang
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Ding-Guo Wang: School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China
Xing Wang: School of Mathematics and Computer Application Technology, Jining University, Qufu 273155, China

Mathematics, 2022, vol. 10, issue 7, 1-23

Abstract: In this paper, we introduce the concept of a generalized Hopf–Ore extension of a Hopf group-coalgebra and give the necessary and sufficient conditions for the Ore extension of a Hopf group-coalgebra to be a Hopf group-coalgebra. Moreover, an isomorphism theorem on generalized Hopf group-coalgebra Ore extensions is given and specific cases in a simple type called special Hopf group-coalgebra Ore extensions are also considered. Our results are generalizations of Hopf–Ore extensions on Hopf algebras and also are very useful to construct new Hopf group-coalgebras.

Keywords: Hopf group-coalgebras; Hopf–Ore extensions; Ore extensions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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