Associative triple trisystems and standard embeddings
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909637187469312 |
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| author | Felipe, Raúl de Salas, Guillermo Vera |
| author_facet | Felipe, Raúl de Salas, Guillermo Vera |
| contents | Building on the established theories of Jordan triple disystems and Leibniz triple systems, we introduce and develop the theory of associative triple trisystems, filling a significant gap in the existing framework. We establish the classical relationships between associative, Jordan, and Lie triple systems within the context of trisystems. We present a significant example by equipping the space of matrices with a non-trivial associative dialgebra structure. We conclude defining the concept of di-endomorphisms of any module, which enables the construction of the standard embedding for any associative triple trisystem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_04191 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Associative triple trisystems and standard embeddings Felipe, Raúl de Salas, Guillermo Vera Rings and Algebras 17A30, 17A60, 17C99 Building on the established theories of Jordan triple disystems and Leibniz triple systems, we introduce and develop the theory of associative triple trisystems, filling a significant gap in the existing framework. We establish the classical relationships between associative, Jordan, and Lie triple systems within the context of trisystems. We present a significant example by equipping the space of matrices with a non-trivial associative dialgebra structure. We conclude defining the concept of di-endomorphisms of any module, which enables the construction of the standard embedding for any associative triple trisystem. |
| title | Associative triple trisystems and standard embeddings |
| topic | Rings and Algebras 17A30, 17A60, 17C99 |
| url | https://arxiv.org/abs/2506.04191 |