doi:10.1007/s13398-026-01851-3engCunha, IsabelElduque, AlbertoJ-ternary algebras, structurable algebras, and Lie superalgebrasART-2026-148815A 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.2026http://zaguan.unizar.es/record/17027110.1007/s13398-026-01851-3http://zaguan.unizar.es/record/170271oai:zaguan.unizar.es:170271info:eu-repo/grantAgreement/ES/DGA/E22-20Rinfo:eu-repo/grantAgreement/ES/MCINN/PID2021-123461NB-C21Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas 120, 3 (2026), [39 pp.]byhttps://creativecommons.org/licenses/by/4.0/deed.esinfo:eu-repo/semantics/openAccess