Linear models of the exceptional Lie algebra $\mathfrak{e}_8$
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916888413470720 |
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| author | Cabrera, Yolanda Draper, Cristina Garvin, Antonio |
| author_facet | Cabrera, Yolanda Draper, Cristina Garvin, Antonio |
| contents | This work provides five explicit constructions of the exceptional Lie algebra $\mathfrak{e}_8$, based on its semisimple subalgebras of maximal rank. Each of these models is graded by an abelian group, namely, $\mathbb{Z}_4$, $\mathbb{Z}_5$, $\mathbb{Z}_6$, $\mathbb{Z}_3^2$ and $\mathbb{Z}_2\times\mathbb{Z}_4$; the neutral component is direct sum of special linear algebras and the remaining homogeneous components are irreducible modules for it. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_09052 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Linear models of the exceptional Lie algebra $\mathfrak{e}_8$ Cabrera, Yolanda Draper, Cristina Garvin, Antonio Rings and Algebras 17B25 (Primary) 17B70 (Secondary) This work provides five explicit constructions of the exceptional Lie algebra $\mathfrak{e}_8$, based on its semisimple subalgebras of maximal rank. Each of these models is graded by an abelian group, namely, $\mathbb{Z}_4$, $\mathbb{Z}_5$, $\mathbb{Z}_6$, $\mathbb{Z}_3^2$ and $\mathbb{Z}_2\times\mathbb{Z}_4$; the neutral component is direct sum of special linear algebras and the remaining homogeneous components are irreducible modules for it. |
| title | Linear models of the exceptional Lie algebra $\mathfrak{e}_8$ |
| topic | Rings and Algebras 17B25 (Primary) 17B70 (Secondary) |
| url | https://arxiv.org/abs/2308.09052 |