摘要
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.
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.
基金
The NSF(A2010000194) of Hebei Province
