An extended Freudenthal Magic Square in characteristic 3

2006/05/15 by Isabel Cunha, Alberto Elduque, Cunha, Isabel +1 · 4 citations
Mathematics · #17B50 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.math/0605379

openalex publication_date 2006/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Freudenthal's Magic Square, which in characteristic 0 contains the exceptional Lie algebras other than G2, is extended over fields of characteristic 3, through the use of symmetric composition superalgebras, to a larger square that contains both Lie algebras and superalgebras. With one exception, the simple Lie superalgebras that appear have no counterpart in characteristic 0.

Citations

• Magic Squares of Lie Algebras

Cited by

• Almost-simple algebraic supergroups
• Exceptionality, Supersymmetry and Non-associativity in Physics
• Semisimplifying Lie algebras of J-ternary algebras in characteristic 3
• J-ternary algebras, structurable algebras, and Lie superalgebras

Related

• The Supermagic Square in characteristic 3 and Jordan superalgebras
• The extended Freudenthal Magic Square and Jordan algebras
• The Magic Square and Symmetric Compositions II
• Magic squares and matrix models of Lie algebras
• Trialities and Exceptional Lie Algebras: DECONSTRUCTING the Magic Square