Iterated Hopf Ore Extensions over Group Rings
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866917267430703104 |
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| author | Hatipoğlu, Can Lomp, Christian |
| author_facet | Hatipoğlu, Can Lomp, Christian |
| contents | We introduce and study a class of Hopf algebras $H(G, χ, η, b, c, β)$ which are two-step Ore extensions of a group algebra $\mathbb{K}[G]$. This construction unifies and generalizes some known families of Hopf algebras such as generalized Taft algebras and Hopf algebras related to $\mathfrak{sl}_2$ constructed by Wang, Wu, and Tan. We analyze the ring theoretical properties of these algebras and classify all finite dimensional simple modules over them. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_10850 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Iterated Hopf Ore Extensions over Group Rings Hatipoğlu, Can Lomp, Christian Rings and Algebras Quantum Algebra Representation Theory 16T05, 17B37, 16G30 We introduce and study a class of Hopf algebras $H(G, χ, η, b, c, β)$ which are two-step Ore extensions of a group algebra $\mathbb{K}[G]$. This construction unifies and generalizes some known families of Hopf algebras such as generalized Taft algebras and Hopf algebras related to $\mathfrak{sl}_2$ constructed by Wang, Wu, and Tan. We analyze the ring theoretical properties of these algebras and classify all finite dimensional simple modules over them. |
| title | Iterated Hopf Ore Extensions over Group Rings |
| topic | Rings and Algebras Quantum Algebra Representation Theory 16T05, 17B37, 16G30 |
| url | https://arxiv.org/abs/2602.10850 |