Jordan algebras and 3-transposition groups

被引：13

作者：

De Medts, Tom ^{[1
]}

Rehren, Felix ^{[2
]}

机构：

[1] Univ Ghent, Dept Math, Krijgslaan 281 S22, B-9000 Ghent, Belgium

[2] Univ Birmingham, Sch Math, Birmingham B15 2TT, W Midlands, England

来源：

JOURNAL OF ALGEBRA | 2017年 / 478卷

关键词：

Jordan algebras; 3-transposition groups; Fischer spaces; Peirce decomposition; Matsuo algebras; Root systems;

D O I：

10.1016/j.jalgebra.2017.01.025

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

An idempotent in a Jordan algebra induces a Peirce decomposition of the algebra into subspaces whose pairwise multiplication satisfies a certain fusion rule Phi)(1/2). On the other hand, 3-transposition groups (G, D) can be algebraically characterised as Matsuo algebras M alpha,(G,D) with idempotents satisfying the fusion rule Phi(a) for some a. We classify the Jordan algebras J which are isomorphic to a Matsuo algebra M-1/2,(G,D), in which case (G,D) is a subgroup of the (algebraic) automorphism group of J; the only possibilities are G = Sym(n) and G = 3(2) : 2. Along the way, we also obtain results about Jordan algebras associated to root systems. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：318 / 340

页数：23