带有不变双线性型的Zinbiel代数

详细信息

Zinbiel algebras with invariant bilinear forms

摘要: Zinbiel代数是与Leibniz代数密切关联的一种代数. 本文研究带有不变双线性型的Zinbiel代数，得到带有这种双线性型的Zinbiel代数的若干性质。利用T*-扩张方法构造新的Zinbiel代数，并给出了T*-扩张等价的充要条件。
- 双模
Abstract: 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.
- bimodule