2024/01/05 by Iván Angiono, Angiono, Iván, Julia Plavnik +3
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2401.02915
We define contragredient Lie algebras in symmetric categories, generalizing the construction of Lie algebras of the form \mathfrakg(A) for a Cartan matrix A from the category of vector spaces to an arbitrary symmetric tensor category. The main complication resides in the fact that, in contrast to the classical case, a general symmetric tensor category can admit tori (playing the role of Cartan subalgebras) which are non-abelian and have a sophisticated representation theory. Using this construction, we obtain and describe new examples of Lie algebras in the universal Verlinde category in characteristic p≥5. We also show that some previously known examples can be obtained with our construction.