Some Braces of Cardinality $p^{4}$ and Related Hopf-Galois Extensions
| Autor: | dora puljic, Agata Smoktunowicz, Kayvan Nejabati Zenouz |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Mathematics::Group Theory
Mathematics::K-Theory and Homology Rings and Algebras (math.RA) Mathematics::Category Theory Mathematics::Quantum Algebra Mathematics - Quantum Algebra Mathematics::Rings and Algebras FOS: Mathematics Quantum Algebra (math.QA) Mathematics - Rings and Algebras Group Theory (math.GR) QA Mathematics - Group Theory |
| Zdroj: | dora puljic |
| ISSN: | 1076-9803 |
| DOI: | 10.48550/arxiv.2106.13735 |
| Popis: | We describe all Fp-braces of cardinality p4 which are not\ud right nilpotent. The constructed braces are solvable and prime and\ud contain a non-zero strongly nilpotent ideal. We use the constructed\ud braces to construct examples of finitely dimensional pre-Lie algebras\ud which are left nilpotent but not right nilpotent. We also explain some\ud well known results about the correspondence between braces and Hopf-Galois extensions using the notion of Hopf-Galois extensions associated to a given brace. This can be applied to the constructed Fp-braces. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|