Zinbiel algebras with invariant bilinear forms

In this paper, we focus on Zinbiel algebras with a kind of bilinear form i.e., invariant bilinear form. We get some properties of Zinbiel algebras with this bilinear form. Moreover a new method of constructing Zinbiel algebras named T*-extensions is studied. We discuss the equivalence of two T*-extensions on a Zinbiel algebra, and give a sufficient and necessary condition for the equivalence.