J-ternary algebras, structurable algebras, and Lie superalgebras

Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas 2026 Open access

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Authors: Isabel Cunha, Alberto Elduque
DOI: 10.1007/s13398-026-01851-3
Cited by: 1
References: 22

Abstract

Abstract A Lie superalgebra is attached to any finite-dimensional J -ternary algebra over an algebraically closed field of characteristic 3, using a process of semisimplification via tensor categories. Some of the exceptional simple Lie algebras, specific of this characteristic, are obtained in this way from J -ternary algebras coming from structurable algebras and, in particular, a new magic square of Lie superalgebras is constructed, with entries depending on a pair of composition algebras.

Fields of Study & Subjects

Advanced Topics in Algebra Algebraic structures and combinatorial models Homotopy and Cohomology in Algebraic Topology

Publication details

Journal / source
Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas
Publisher
Springer Science and Business Media LLC
Volume
120
Issue
3
Publication date
2 April 2026
Language
EN