Some equivalent conditions for double Frobenius algebras to be strict ones are given. Then some examples of （strict or non-strict） double Frobenius algebras are presented. Finally, a sufficient and necessary conditi...Some equivalent conditions for double Frobenius algebras to be strict ones are given. Then some examples of （strict or non-strict） double Frobenius algebras are presented. Finally, a sufficient and necessary condition for the trivial extension of a double Frobenius algebra to be a （strict） double Frobenius algebra is given.展开更多
LEFT-symmetric algebra is a new kind of algebra system obtained from the studying of Lie al-gebra, Lie group and differential geometry. It is very useful for many topics in geometry andalgebra. In this note, we discus...LEFT-symmetric algebra is a new kind of algebra system obtained from the studying of Lie al-gebra, Lie group and differential geometry. It is very useful for many topics in geometry andalgebra. In this note, we discuss a special kind of left-symmetric algebra which is verymeaningful--bi-symmetric algebra.展开更多
基金This work was supported by the National Natural Science Foundation of China （Grant No. 11471282）, the China Postdoctoral Science Foundation （Grant No. 2017M610316）, and the Natural Science Foundation of Jiangsu Province （Grant No. BK20170589）.
文摘Some equivalent conditions for double Frobenius algebras to be strict ones are given. Then some examples of （strict or non-strict） double Frobenius algebras are presented. Finally, a sufficient and necessary condition for the trivial extension of a double Frobenius algebra to be a （strict） double Frobenius algebra is given.
文摘LEFT-symmetric algebra is a new kind of algebra system obtained from the studying of Lie al-gebra, Lie group and differential geometry. It is very useful for many topics in geometry andalgebra. In this note, we discuss a special kind of left-symmetric algebra which is verymeaningful--bi-symmetric algebra.
