Isomorphisms of Tits--Kantor--Koecher Lie algebras of JB*-triples
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866910900514979840 |
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| author | Cueto-Avellaneda, María Oliveira, Lina |
| author_facet | Cueto-Avellaneda, María Oliveira, Lina |
| contents | We characterise the isomorphisms of Tits--Kantor--Koecher Lie algebras of JB*-triples as a class of surjective linear isometries and show how these algebras form a category equivalent to that of JB*-triples. We introduce the concepts of tripotent, and orthogonality and order amongst tripotents for Tits--Kantor--Koecher Lie algebras. This leads to showing that a graded or negatively graded order isomorphism between certain subsets of tripotents of two Tits--Kantor--Koecher Lie algebras of atomic JB*-triples, which commutes with involutions, preserves orthogonality and is continuous at a non-zero tripotent of a specific type, can be extended as a real-linear isomorphism between the algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_00534 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Isomorphisms of Tits--Kantor--Koecher Lie algebras of JB*-triples Cueto-Avellaneda, María Oliveira, Lina Functional Analysis We characterise the isomorphisms of Tits--Kantor--Koecher Lie algebras of JB*-triples as a class of surjective linear isometries and show how these algebras form a category equivalent to that of JB*-triples. We introduce the concepts of tripotent, and orthogonality and order amongst tripotents for Tits--Kantor--Koecher Lie algebras. This leads to showing that a graded or negatively graded order isomorphism between certain subsets of tripotents of two Tits--Kantor--Koecher Lie algebras of atomic JB*-triples, which commutes with involutions, preserves orthogonality and is continuous at a non-zero tripotent of a specific type, can be extended as a real-linear isomorphism between the algebras. |
| title | Isomorphisms of Tits--Kantor--Koecher Lie algebras of JB*-triples |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2504.00534 |