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
In this article, we discuss some properties of a supersymmetric invariant bilinear form on Lie supertriple systems. In particular, a supersymmetric invariant bilinear form on Lie supertriple systems can be extended to...In this article, we discuss some properties of a supersymmetric invariant bilinear form on Lie supertriple systems. In particular, a supersymmetric invariant bilinear form on Lie supertriple systems can be extended to its standard imbedding Lie superalgebras. Furthermore, we generalize Garland＇s theory of universal central extensions for Lie supertriple systems following the classical one for Lie superalgebras. We solve the problems of lifting automorphisms and lifting derivations.展开更多
In the present paper, we develop initially the Frattini theory for Lie supertriple systems, obtain some properties of the Frattini subsystem and show that the intersection of all maximal subsystems of a solvable Lie s...In the present paper, we develop initially the Frattini theory for Lie supertriple systems, obtain some properties of the Frattini subsystem and show that the intersection of all maximal subsystems of a solvable Lie supertriple system is its ideal. Moreover, we give the relationship between φ-free and complemented for Lie supertriple system.展开更多
In this article, we study the Lie supertriple system （LSTS） T over a field K admitting a nondegenerate invariant supersymmetric bilinear form （call such a Tmetrisable）. We give the definition of T＊ω-extension of...In this article, we study the Lie supertriple system （LSTS） T over a field K admitting a nondegenerate invariant supersymmetric bilinear form （call such a Tmetrisable）. We give the definition of T＊ω-extension of an LSTS T , prove a necessary and sufficient condition for a metrised LSTS （T ,Ф） to be isometric to a T＊-extension of some LSTS, and determine when two T＊-extensions of an LSTS are ＂same＂, i.e., they are equivalent or isometrically equivalent.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.
基金supported by the NSFC(10871057)NSFJL(20130101068JC)supported by Fundamental Research Funds for the Central Universities of China and SRFHLJED(12521157)
文摘In this article, we discuss some properties of a supersymmetric invariant bilinear form on Lie supertriple systems. In particular, a supersymmetric invariant bilinear form on Lie supertriple systems can be extended to its standard imbedding Lie superalgebras. Furthermore, we generalize Garland＇s theory of universal central extensions for Lie supertriple systems following the classical one for Lie superalgebras. We solve the problems of lifting automorphisms and lifting derivations.
基金Supported by the National Natural Science Foundation of China (Grant Nos. 10701019 10871057)
文摘In the present paper, we develop initially the Frattini theory for Lie supertriple systems, obtain some properties of the Frattini subsystem and show that the intersection of all maximal subsystems of a solvable Lie supertriple system is its ideal. Moreover, we give the relationship between φ-free and complemented for Lie supertriple system.
文摘In this article, we study the Lie supertriple system （LSTS） T over a field K admitting a nondegenerate invariant supersymmetric bilinear form （call such a Tmetrisable）. We give the definition of T＊ω-extension of an LSTS T , prove a necessary and sufficient condition for a metrised LSTS （T ,Ф） to be isometric to a T＊-extension of some LSTS, and determine when two T＊-extensions of an LSTS are ＂same＂, i.e., they are equivalent or isometrically equivalent.
