Work

Lie algebras in symmetric tensor categories

Year: 2026

Type: preprint

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 $\mathcal{O}$, 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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.27492

Authors: Angiono, Iván, Czenky, Agustina, Etingof, Pavel, Ostrik, Victor, Plavnik, Julia, Sanmarco, Guillermo

Institutions: Consejo Nacional de Investigaciones Científicas y Técnicas, Universidad Nacional de Córdoba, University of Southern California

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, American Institute of Mathematics, Science Foundation Ireland, Consejo Nacional de Investigaciones Científicas y Técnicas

Award: Tensor categories, quantized algebras, and the analytic Langlands correspondence

OpenAlex ID: W7223148300

Cites: 6

Cited by:

Related to: 10