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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2309.12451 |
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| _version_ | 1866916292369317888 |
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| author | Angiono, Iván Plavnik, Julia Sanmarco, Guillermo |
| author_facet | Angiono, Iván Plavnik, Julia Sanmarco, Guillermo |
| contents | We describe the structure and different features of Lie algebras in the Verlinde category, obtained as semisimplification of contragredient Lie algebras in characteristic $p$ with respect to the adjoint action of a Chevalley generator. In particular, we construct a root system for these algebras that arises as a parabolic restriction of the known root system for the classical Lie algebra. This gives a lattice grading with simple homogeneous components and a triangular decomposition for the semisimplified Lie algebra. We also obtain a non-degenerate invariant form that behaves well with the lattice grading. As an application, we exhibit concrete new examples of Lie algebras in the Verlinde category. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_12451 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Semisimplification of contragredient Lie algebras Angiono, Iván Plavnik, Julia Sanmarco, Guillermo Representation Theory 18M05, 17B50, 17B67 We describe the structure and different features of Lie algebras in the Verlinde category, obtained as semisimplification of contragredient Lie algebras in characteristic $p$ with respect to the adjoint action of a Chevalley generator. In particular, we construct a root system for these algebras that arises as a parabolic restriction of the known root system for the classical Lie algebra. This gives a lattice grading with simple homogeneous components and a triangular decomposition for the semisimplified Lie algebra. We also obtain a non-degenerate invariant form that behaves well with the lattice grading. As an application, we exhibit concrete new examples of Lie algebras in the Verlinde category. |
| title | Semisimplification of contragredient Lie algebras |
| topic | Representation Theory 18M05, 17B50, 17B67 |
| url | https://arxiv.org/abs/2309.12451 |