Rota-Baxter Operators On The Four-Dimensional Interleaved Algebra And Its Associated Conclusions

In this master thesis,we focus on the Rota-Baxter operators of four-dimensional alternative algebras and obtain several conclusioens related to the algebra.First,using the definition of Rota-Baxter operator and the structure of such thought alternative algebras.In this paper,we determine the complete classification of Rota-Baxter operators on such alternative algebras.Second,according to the determined Rota-Baxter operators.In this master thesis,we characterize the solutions of the alternative Yang-Baxter equation on the eight-dimensional alternative algebra corresponding to each class of Rota-Baxter operators.Third,using the Rota-Baxter operator on the obtained four-dimensional alternative algebra.We construct pre-alternative algebras on such alternative algebras;Finally,using the relationship between the alternative and pre-alternative algebra,we obtain the alternative algebras on the purchased pre-alternative algebras and verify whether these alternative algebras are associative algebras.