On Integrable Roots in Split Lie Triple Systems

<正> We focus on the notion of an integrable root in the framework of split Lie triple systemsT with a coherent 0-root space. As a main result, it is shown that if T has all its nonzero rootsintegrable, 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 allnonzero roots of T are integrable then T is locally finite, is stated. Finally, a classification theorem forsplit simple Lie triple systems having all its nonzero roots integrable is given.