Group schemes and their Lie algebras over a symmetric tensor category
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909674250436608 |
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| author | Benson, Dave Pevtsova, Julia |
| author_facet | Benson, Dave Pevtsova, Julia |
| contents | We investigate the theory of affine group schemes over a symmetric tensor category, with particular attention to the tangent space at the identity. We show that this carries the structure of a restricted Lie algebra, and can be viewed as the degree one distributions on the group scheme, or as the right invariant derivations on the coordinate ring. In the second half of the paper, we illustrate the theory in the particular case of the symmetric tensor category $\mathsf{Ver}_4^+$ in characteristic two. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_02031 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Group schemes and their Lie algebras over a symmetric tensor category Benson, Dave Pevtsova, Julia Representation Theory Category Theory Quantum Algebra 18D10 (primary), 14L15, 17B45, 18M05, 18M20 (secondary) We investigate the theory of affine group schemes over a symmetric tensor category, with particular attention to the tangent space at the identity. We show that this carries the structure of a restricted Lie algebra, and can be viewed as the degree one distributions on the group scheme, or as the right invariant derivations on the coordinate ring. In the second half of the paper, we illustrate the theory in the particular case of the symmetric tensor category $\mathsf{Ver}_4^+$ in characteristic two. |
| title | Group schemes and their Lie algebras over a symmetric tensor category |
| topic | Representation Theory Category Theory Quantum Algebra 18D10 (primary), 14L15, 17B45, 18M05, 18M20 (secondary) |
| url | https://arxiv.org/abs/2507.02031 |