Hopf代数的Drinfeld理论在求解量子Yang-Baxter方程（QYBE）等方面有着重要的作用。非结合Hopf代数作为Hopf代数的一种推广，建立并研究其上的Drinfeld理论是很有价值的。本项目将研究非结合Hopf代数的Drinfeld理论及其应用。首先，引入拟三角非结合Hopf代数的概念，给出拟三角非结合Hopf代数的结构定理，探究其在求解QYBE、构造量子不变量中的应用。其次，对非结合Hopf代数的Drinfeld量子偶和Drinfeld扭曲理论展开研究，拓宽非结合Hopf代数例子来源。探讨其模范畴和量子偶上的Yetter-Drinfeld模范畴的联系，给出相应QYBE的解的分解。最后，结合非结合Hopf代数的Drinfeld理论到求解若干非线性方程进行研究，给出相应FRT构造定理，并对由此方法所得到的非结合Hopf代数的结构性质及应用进行讨论。

Drinfeld theory of Hopf algebras plays an importent role in solving quantum Yang-Baxter equation (QYBE).Non-associative Hopf algebras are an interesting new generalization of Hopf algebras and henceit is worthwhile to see how much of the Drinfeld theory goes through in their case. The aim of this project is to study the Drinfeld theory of non-associative Hopf algebras and its applications. Mainly included: 1. Introduce the concepts of quasitriangular non-associative Hopf algebras and construct some examples. Give structures theorem and basic properties for quasitriangular non-associative Hopf algebras. Investigate the applications of quasitriangular structure in finding solutions of QYBE and constructing quantum invariants; 2. Construct and study Drinfeld quantum double and Drinfeld twists theory, in order to find more examples of quasitriangular non-associative Hopf algebras. Make clear the relationship between the module category of a non-associative Hopf algebra and Yetter-Drinfeld module category of Drinfeld quantum double. Then try to find the possibility to factorize the R-matrix corresponding to the solution of the Yang-Baxter equation associated with a quasitriangular non-associative Hopf algebra; 3. Connect the Drinfeld theory of non-associative Hopf algebras to the study of QYBE and other nonlinear equations. For all these equations, we will give the versions of FRT theorem, and then discuss the structure properties and its applications of the non-associative Hopf algebras obtained in this way.