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PreprintCC BY 4.0arXiv

Lie algebras in symmetric tensor categories

  • Iván Angiono
  • Agustina Czenky
  • Pavel Etingof
  • Victor Ostrik
  • Julia Plavnik
  • Guillermo Sanmarco
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Abstract

We develop the general theory of Lie algebras in symmetric tensor categories. We prove categorical versions of classical results such as Engel's theorem, Cartan's criterion, and that all derivations of a strongly semisimple Lie algebra are inner. For finite-dimensional graded Lie algebras, we construct a graded category 𝒪, classify its graded-simple objects, and prove the generic graded irreducibility of Verma modules. Lastly, we develop the theory of root systems for contragredient Lie algebras.

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Cite

BibTeXRIS
BibTeX
@misc{angiono2026algebras,
  title = {{Lie algebras in symmetric tensor categories}},
  author = {Iván Angiono and Agustina Czenky and Pavel Etingof and Victor Ostrik and Julia Plavnik and Guillermo Sanmarco},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.27492},
  eprint = {2610.27492},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.27492},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Lie algebras in symmetric tensor categories
AU  - Iván Angiono
AU  - Agustina Czenky
AU  - Pavel Etingof
AU  - Victor Ostrik
AU  - Julia Plavnik
AU  - Guillermo Sanmarco
PY  - 2026
DA  - 2026/10/20
PB  - arXiv
DO  - 10.48550/arxiv.2610.27492
UR  - https://arxiv.org/abs/2610.27492
AB  - We develop the general theory of Lie algebras in symmetric tensor categories. We prove categorical versions of classical results such as Engel's theorem, Cartan's criterion, and that all derivations of a strongly semisimple Lie algebra are inner. For finite-dimensional graded Lie algebras, we construct a graded category 𝒪, classify its graded-simple objects, and prove the generic graded irreducibility of Verma modules. Lastly, we develop the theory of root systems for contragredient Lie algebras.
ER  -