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...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-04-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/7/1167 |
| _version_ | 1827623105509457920 |
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| author | Ding-Guo Wang Xing Wang |
| author_facet | Ding-Guo Wang Xing Wang |
| author_sort | Ding-Guo Wang |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-09T11:38:45Z |
| format | Article |
| id | doaj.art-f452a007b37346d0abc2457162a941b3 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T11:38:45Z |
| publishDate | 2022-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-f452a007b37346d0abc2457162a941b32023-11-30T23:38:08ZengMDPI AGMathematics2227-73902022-04-01107116710.3390/math10071167Generalized Hopf–Ore Extensions of Hopf Group-CoalgebrasDing-Guo Wang0Xing Wang1School of Mathematical Sciences, Qufu Normal University, Qufu 273165, ChinaSchool of Mathematics and Computer Application Technology, Jining University, Qufu 273155, ChinaIn 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.https://www.mdpi.com/2227-7390/10/7/1167Hopf group-coalgebrasHopf–Ore extensionsOre extensions |
| spellingShingle | Ding-Guo Wang Xing Wang Generalized Hopf–Ore Extensions of Hopf Group-Coalgebras Mathematics Hopf group-coalgebras Hopf–Ore extensions Ore extensions |
| title | Generalized Hopf–Ore Extensions of Hopf Group-Coalgebras |
| title_full | Generalized Hopf–Ore Extensions of Hopf Group-Coalgebras |
| title_fullStr | Generalized Hopf–Ore Extensions of Hopf Group-Coalgebras |
| title_full_unstemmed | Generalized Hopf–Ore Extensions of Hopf Group-Coalgebras |
| title_short | Generalized Hopf–Ore Extensions of Hopf Group-Coalgebras |
| title_sort | generalized hopf ore extensions of hopf group coalgebras |
| topic | Hopf group-coalgebras Hopf–Ore extensions Ore extensions |
| url | https://www.mdpi.com/2227-7390/10/7/1167 |
| work_keys_str_mv | AT dingguowang generalizedhopforeextensionsofhopfgroupcoalgebras AT xingwang generalizedhopforeextensionsofhopfgroupcoalgebras |