Graded contractions on the orthogonal Lie algebras of dimensions 7 and 8
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866908482985263104 |
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| author | Draper, Cristina Meyer, Thomas Leenen Sánchez-Ortega, Juana |
| author_facet | Draper, Cristina Meyer, Thomas Leenen Sánchez-Ortega, Juana |
| contents | Graded contractions of certain non-toral $\mathbb{Z}_2^3$-gradings on the simple Lie algebras $\mathfrak{so}(7,\mathbb C)$ and $\f{so}(8,\mathbb C)$ are classified up to two notions of equivalence. In particular, there arise two large families of Lie algebras (the majority of which are solvable) of dimensions 21 and 28. This is achieved as a significant generalization of the classification of related graded contractions on $\mathfrak g_2$, the derivation algebra of the octonion algebra. Many of the results can be further extended to any \emph{good} $\mathbb Z_2^3$-grading on an arbitrary Lie algebra. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_18069 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Graded contractions on the orthogonal Lie algebras of dimensions 7 and 8 Draper, Cristina Meyer, Thomas Leenen Sánchez-Ortega, Juana Rings and Algebras Mathematical Physics 17B70, 17B30, 17B81 Graded contractions of certain non-toral $\mathbb{Z}_2^3$-gradings on the simple Lie algebras $\mathfrak{so}(7,\mathbb C)$ and $\f{so}(8,\mathbb C)$ are classified up to two notions of equivalence. In particular, there arise two large families of Lie algebras (the majority of which are solvable) of dimensions 21 and 28. This is achieved as a significant generalization of the classification of related graded contractions on $\mathfrak g_2$, the derivation algebra of the octonion algebra. Many of the results can be further extended to any \emph{good} $\mathbb Z_2^3$-grading on an arbitrary Lie algebra. |
| title | Graded contractions on the orthogonal Lie algebras of dimensions 7 and 8 |
| topic | Rings and Algebras Mathematical Physics 17B70, 17B30, 17B81 |
| url | https://arxiv.org/abs/2409.18069 |