On Integrable Roots in Split Lie Triple Systems  

作　　者：A.J.CALDERóN MARTíN 

机构地区：[1]Departamento de Matemáticas, Universidad de Cádiz

出　　处：《Acta Mathematica Sinica,English Series》2009年第11期1759-1774,共16页数学学报（英文版）

基　　金：the PCI of the UCA‘Teoría de Lie y Teoría de Espacios de Banach’,by the PAI's with project numbers FQM-298,FQM-3737,FQM-02467;the project of the Spanish Ministerio de Educación y Ciencia MTM2004-06580-C02-02 and with rondos FEDER

摘　　要：We focus on the notion of an integrable root in the framework of split Lie triple systems T with a coherent 0-root space. As a main result, it is shown that if T has all its nonzero roots integrable, then its standard embedding is a split Lie algebra having all its nonzero roots integrable. As a consequence, a local finiteness theorem for split Lie triple systems, saying that whenever all nonzero roots of T are integrable then T is locally finite, is stated. Finally, a classification theorem for split simple Lie triple systems having all its nonzero roots integrable is given.We focus on the notion of an integrable root in the framework of split Lie triple systems T with a coherent 0-root space. As a main result, it is shown that if T has all its nonzero roots integrable, then its standard embedding is a split Lie algebra having all its nonzero roots integrable. As a consequence, a local finiteness theorem for split Lie triple systems, saying that whenever all nonzero roots of T are integrable then T is locally finite, is stated. Finally, a classification theorem for split simple Lie triple systems having all its nonzero roots integrable is given.

关 键 词：Lie triple system ROOT split Lie algebra classification theory 

分 类 号：O152.5[理学—数学] O152.1[理学—基础数学]