Tate-Shafarevich groups and algebras
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866909668654186496 |
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| author | Kunyavskii, Boris Ostapenko, Vadim Z. |
| author_facet | Kunyavskii, Boris Ostapenko, Vadim Z. |
| contents | The Tate-Shafarevich set of a group G defined by Takashi Ono coincides, in the case where G is finite, with the group of outer class-preserving automorphisms of G introduced by Burnside. We consider analogues of this important group-theoretic object for Lie algebras and associative algebras and establish some new structure properties thereof. We also discuss open problems and eventual generalizations to other algebraic structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_05406 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Tate-Shafarevich groups and algebras Kunyavskii, Boris Ostapenko, Vadim Z. Group Theory Rings and Algebras 17B40 17B56 20J06 22E60 The Tate-Shafarevich set of a group G defined by Takashi Ono coincides, in the case where G is finite, with the group of outer class-preserving automorphisms of G introduced by Burnside. We consider analogues of this important group-theoretic object for Lie algebras and associative algebras and establish some new structure properties thereof. We also discuss open problems and eventual generalizations to other algebraic structures. |
| title | Tate-Shafarevich groups and algebras |
| topic | Group Theory Rings and Algebras 17B40 17B56 20J06 22E60 |
| url | https://arxiv.org/abs/2211.05406 |