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.