In this article, the Killing form of a Lie supertriple system （LSTS） and that of its imbedding Lie superalgebra （LSA） are investigated, and a unique decomposition theorem for a quasiclassical LSTS with trivial cen...In this article, the Killing form of a Lie supertriple system （LSTS） and that of its imbedding Lie superalgebra （LSA） are investigated, and a unique decomposition theorem for a quasiclassical LSTS with trivial center is established by means of the parallel decomposition theorem for a quasiclassical LSA.展开更多
We investigate the nilpotence of a Malcev algebra M and of its standard enveloping Lie algebra L(M) = M(?)D(M, M). The main result shows that an ideal A of M is nilpotent in M if and only if the corresponding ideal I(...We investigate the nilpotence of a Malcev algebra M and of its standard enveloping Lie algebra L(M) = M(?)D(M, M). The main result shows that an ideal A of M is nilpotent in M if and only if the corresponding ideal I(A) = A(?)D(A, M) is nilpotent in L(M).展开更多
For Lie triple systems in the characteristic zero setting, we obtain by means of the Killing forms two criterions for semisimplicity and for solvability respectively, and then investigate the relationship among the Ki...For Lie triple systems in the characteristic zero setting, we obtain by means of the Killing forms two criterions for semisimplicity and for solvability respectively, and then investigate the relationship among the Killing forms of a real Lie triple system To, the complexification T of To, and the realification of T.展开更多
基金Supported by the Natural Science Foundation of Hebei Province of China(A2005000088)
文摘In this article, the Killing form of a Lie supertriple system （LSTS） and that of its imbedding Lie superalgebra （LSA） are investigated, and a unique decomposition theorem for a quasiclassical LSTS with trivial center is established by means of the parallel decomposition theorem for a quasiclassical LSA.
文摘We investigate the nilpotence of a Malcev algebra M and of its standard enveloping Lie algebra L(M) = M(?)D(M, M). The main result shows that an ideal A of M is nilpotent in M if and only if the corresponding ideal I(A) = A(?)D(A, M) is nilpotent in L(M).
基金the Natural Science Foundation of Hebei Province (Nos.A200500008A2007000138)
文摘For Lie triple systems in the characteristic zero setting, we obtain by means of the Killing forms two criterions for semisimplicity and for solvability respectively, and then investigate the relationship among the Killing forms of a real Lie triple system To, the complexification T of To, and the realification of T.
