We study the structure of arbitrary split Leibniz triple systems with a coherent O-root space. By developing techniques of connections of roots for this kind of triple systems, under certain conditions, in the case of...We study the structure of arbitrary split Leibniz triple systems with a coherent O-root space. By developing techniques of connections of roots for this kind of triple systems, under certain conditions, in the case of T being of maximal length＇, the simplicity of the Leibniz triple systems is characterized.展开更多
We introduce elementary and Ф-free Lie triple systems and study the properties of these systems. In particular, structures of subsystems of an elementary Lie triple system and a class of Ф-free Lie triple systems ar...We introduce elementary and Ф-free Lie triple systems and study the properties of these systems. In particular, structures of subsystems of an elementary Lie triple system and a class of Ф-free Lie triple systems are investigated.展开更多
Let S be a nonassociative k-algebra. By using the Lie triple system, we study the subspace I2（S） of the Steinberg Lie algebra st2（S） and give a necessary and sufficient condition for I2（S） = 0.
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...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.展开更多
For a Lie triple system T over a field of characteristic zero, some sufficient conditions for T to be two-generated are proved. We also discuss to what extent the two-generated subsystems determine the structure of th...For a Lie triple system T over a field of characteristic zero, some sufficient conditions for T to be two-generated are proved. We also discuss to what extent the two-generated subsystems determine the structure of the system T . One of the main results is that T is solvable if and only if every two elements generates a solvable subsystem. In fact, we give an explicit two-generated law for the two-generated subsystems.展开更多
We gave a complete list of totally geodesic submanifolds of maximal rank in symmetric spaces of noncompact type. The compact cases can be obtained by the duality.
In this paper, the authors define the center of a Symplectic ternary algebra, and investigate the relationship between the center of a Symplectic ternary algebra and that of the Lie triple system associated with it. A...In this paper, the authors define the center of a Symplectic ternary algebra, and investigate the relationship between the center of a Symplectic ternary algebra and that of the Lie triple system associated with it. As an application of the relationship, the unique decomposition theorem for Symplectic ternary algebras with trivial center is obtained.展开更多
基金Supported by Scientific Research Fund of Heilongjiang Provincial Education Department(Grant No.12541184)
文摘We study the structure of arbitrary split Leibniz triple systems with a coherent O-root space. By developing techniques of connections of roots for this kind of triple systems, under certain conditions, in the case of T being of maximal length＇, the simplicity of the Leibniz triple systems is characterized.
基金supported in part by the National Natural Science Foundation of China(10871192)NSF(A2010000194) of Hebei Province,China
文摘We introduce elementary and Ф-free Lie triple systems and study the properties of these systems. In particular, structures of subsystems of an elementary Lie triple system and a class of Ф-free Lie triple systems are investigated.
基金The second author is supported in part by the National Natural Science Foundation of China （11101387 and 10971104）, the Anhui Provincial Natural Science Foundation （1208085MA01） and the Fundamental Research Funds for the Central Universities （WK 0010000023）. The third author is supported in part by NSERC of Canada and Chinese Academy of Science.
文摘Let S be a nonassociative k-algebra. By using the Lie triple system, we study the subspace I2（S） of the Steinberg Lie algebra st2（S） and give a necessary and sufficient condition for I2（S） = 0.
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-02467the project of the Spanish Ministerio de Educación y Ciencia MTM2004-06580-C02-02 and with rondos FEDER
文摘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.
文摘For a Lie triple system T over a field of characteristic zero, some sufficient conditions for T to be two-generated are proved. We also discuss to what extent the two-generated subsystems determine the structure of the system T . One of the main results is that T is solvable if and only if every two elements generates a solvable subsystem. In fact, we give an explicit two-generated law for the two-generated subsystems.
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.10171048&10271058).
文摘We gave a complete list of totally geodesic submanifolds of maximal rank in symmetric spaces of noncompact type. The compact cases can be obtained by the duality.
基金Supported by the National Natural Science Foundation of China (Grant No. 10871192)
文摘In this paper, the authors define the center of a Symplectic ternary algebra, and investigate the relationship between the center of a Symplectic ternary algebra and that of the Lie triple system associated with it. As an application of the relationship, the unique decomposition theorem for Symplectic ternary algebras with trivial center is obtained.
