Generalized Hopf–Ore Extensions of Hopf Group-Coalgebras
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 Or...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-04-01
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| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/10/7/1167 |
| Summary: | 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. |
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| ISSN: | 2227-7390 |