Work

J-ternary algebras, structurable algebras, and Lie superalgebras

Year: 2025

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2506.18486

Authors: Cunha, Isabel, Elduque, Alberto

Institutions: University of Beira Interior, Universidad de Zaragoza, Centro de Matemática e Aplicações, Instituto Universitario de Matemáticas y Aplicaciones

Language: English

Topic: Advanced Topics in Algebra

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W6891839892

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