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
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
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.
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.
