带有不变双线性型的Zinbiel代数

Zinbiel Algebras with Invariant Bilinear Forms

研究了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,并且讨论了同态的2个Zinbiel代数的不变双线性型的关系.另外,通过合理定义Zinbiel代数上的双模、2-上循环,提出了构造新的Zinbie代数扩张方法(T*-扩张),并给出在同一Zinbie代数上得到的2个不同的T*-扩张等价的充要条件,且得到了Zinbiel代数与其T*-扩张代数的幂零指标的关系.

A study of Zinbiel algebras with invariant bilinear forms is presented. Some properties of these Zinbiel algebras are obtained. The relationship between two similar Zinbiel algebras＇ invariant bilinear forms is discussed,and a new method of constructing Zinbiel algebras is put forward with T＊-entension based on reasonable definitions of bimodule and 2-cocycle. The sufficient and necessary condition for the equivalence of two T＊-extensions on the same Zinbiel algebra is worked out,and the relationship of nilpotency indexs between Zinbiel algebras and their T＊-extensions is identified.