2024/07/15 by Tom De Medts, De Medts, Tom, Jeroen Meulewaeter +1
Mathematics · #17A30 #17B05 #17B20 #17B25 #17B40 #17B45 #17B60 #17C40 #20G15 #20G41 #51A50 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2407.10672
openalex publication_date 2024/07/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study simple Lie algebras generated by extremal elements, over arbitrary fields of arbitrary characteristic. We show: (1) If the extremal geometry contains lines, then the Lie algebra admits a 5 × 5-grading that can be parametrized by a cubic norm structure; (2) If there exists a field extension of degree at most 2 such that the extremal geometry over that field extension contains lines, and in addition, there exist symplectic pairs of extremal elements, then the Lie algebra admits a 5 × 5-grading that can be parametrized by a quadrangular algebra. One of our key tools is a new definition of exponential maps that makes sense even over fields of characteristic 2 and 3, which ought to be interesting in its own right.