Structure and Representation Theory of basic simple $\mathbb{Z}_2\times \mathbb{Z}_2$-graded color Lie algebras
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908923079950336 |
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| author | Afentoulidis-Almpanis, Spyridon |
| author_facet | Afentoulidis-Almpanis, Spyridon |
| contents | We adapt methods from the theory of complex semisimple Lie algebras to develop a root theory for a class of simple $\mathbb{Z}_2 \times \mathbb{Z}_2$-graded (color) Lie algebras, which we call basic. As an application, assuming that the Cartan subalgebra is self-centralizing, we classify all finite-dimensional representations of these algebras by proving a highest weight theorem and a complete reducibility theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_08986 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Structure and Representation Theory of basic simple $\mathbb{Z}_2\times \mathbb{Z}_2$-graded color Lie algebras Afentoulidis-Almpanis, Spyridon Representation Theory Mathematical Physics Primary 17B75, Secondary 17B81, 17B22 We adapt methods from the theory of complex semisimple Lie algebras to develop a root theory for a class of simple $\mathbb{Z}_2 \times \mathbb{Z}_2$-graded (color) Lie algebras, which we call basic. As an application, assuming that the Cartan subalgebra is self-centralizing, we classify all finite-dimensional representations of these algebras by proving a highest weight theorem and a complete reducibility theorem. |
| title | Structure and Representation Theory of basic simple $\mathbb{Z}_2\times \mathbb{Z}_2$-graded color Lie algebras |
| topic | Representation Theory Mathematical Physics Primary 17B75, Secondary 17B81, 17B22 |
| url | https://arxiv.org/abs/2603.08986 |