2025/09/02 by Akihide Hanaki, Hanaki, Akihide, Masayoshi Yoshikawa +1
Mathematics · #05E30 #05E99 #17C20 #Advanced Topics in Algebra #Algebraic and Geometric Analysis #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2509.01865
openalex publication_date 2025/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a construction of a Jordan scheme from an elementary abelian 2-group of rank n and a \1,-1\-matrix of order 2n that satisfies a specified condition. We then prove that the orders of matrices with the specified condition are limited to 2, 4 or 8. Using these matrices, we construct essentially two new proper Jordan schemes of orders 16 and 32. Finally, we analyze the structures of the real adjacency Jordan algebras of these Jordan schemes and prove that they are the first known examples whose real adjacency Jordan algebras admit simple components of type ℝ ⊕f ℝn, namely non-Hermitian type.