Semisimplifying Lie algebras of J -ternary algebras in characteristic 3
Abstract
We describe a class of Lie superalgebras in characteristic 3, containing the Elduque-Cunha superalgebras g(3,3),g(6,6) and the Elduque superalgebra el(5,3), using the tensor product of composition algebras. For the Lie superalgebra el(5,3), this allows us to move beyond the contragredient construction and it also allows us to construct more general forms.We also describe how one obtains these Lie superalgebras using the semisimplification functor on the representation category Rep(α3) to Lie algebras of type E6, E7 and E8, in line with how Arun Kannan applied this functor to the split algebras. We further apply this functor more broadly to the class of Lie algebras coming from J-ternary algebras over fields of characteristic 3.
Fields of Study & Subjects
Advanced Topics in Algebra
Algebraic structures and combinatorial models
Homotopy and Cohomology in Algebraic Topology
Publication details
- Journal / source
- Communications in Algebra
- Publisher
- Informa UK Limited
- Volume
- 54
- Issue
- 9
- Pages
- 3233–3249
- Publication date
- 1 January 2026
- Language
- EN