标题： 反预诺维科夫代数，准三角形和可分解的反预诺维科夫双代数 显示英文标题

标题： Anti-pre-Novikov algebras, quasi-triangular and factorizable anti-pre-Novikov bialgebras

摘要： 首先，我们引入了反-前-Novikov代数的概念，作为分解Novikov代数的新框架。 在Novikov代数上的反-O-算子被开发出来，以提供构造反-前-Novikov代数的代数框架。 其次，我们引入了反-前-Novikov双代数的概念，作为对称拟-Frobenius Novikov代数双构造对应的双代数结构，该结构由Novikov代数的某些匹配对以及相容的反-前-Novikov代数来表征。 对上同调情况的研究导致了反-前-Novikov Yang-Baxter方程（APN-YBE），其斜对称解产生上同调反-前-Novikov双代数。 研究了反-前-Novikov代数上的O-算子，以构造APN-YBE的斜对称解。 第三，我们研究了准三角形和可分解的反-前-Novikov双代数，作为上同调反-前-Novikov双代数的一个特殊类。 APN-YBE的解，其对称部分是不变的，产生准三角形反-前-Novikov双代数。 此外，引入了带有权值的相对Rota-Baxter算子，以展示APN-YBE的解，其对称部分是不变的。 最后，我们引入了二次Rota-Baxter反-前-Novikov代数的概念，它与可分解的反-前-Novikov双代数一一对应。 显示英文摘要

摘要： Firstly, we introduce a notion of anti-pre-Novikov algebras as a new framework for decomposing Novikov algebras. Anti-O-operators on Novikov algebras are developed to provide an algebraic framework for constructing anti-pre-Novikov algebras. Secondly, we introduce a notion of anti-pre-Novikov bialgebras as the bialgebra structures corresponding to a double construction of symmetric quasi-Frobenius Novikov algebras, which is characterized by certain matched pairs of Novikov algebras as well as the compatible anti-pre-Novikov algebras. The study of the coboundary case induces the anti-pre-Novikov Yang-Baxter equation (APN-YBE), whose skew-symmetric solutions yield coboundary anti-pre-Novikov bialgebras. The notion of O-operators on anti-pre-Novikov algebras is studied to construct skew-symmetric solutions of the APN-YBE. Thirdly, we investigate quasi-triangular and factorizable anti-pre-Novikov bialgebras as a special class of coboundary anti-pre-Novikov bialgebras. The solutions of the APN-YBE whose symmetric parts are invariant give rise to a quasi-triangular anti-pre-Novikov bialgebra. Moreover, relative Rota-Baxter operators with weights are introduced to demonstrate solutions of the APN-YBE whose symmetric parts are invariant. Finally, we introduce a notion of quadratic Rota-Baxter anti-pre-Novikov algebras, which is one to one correspondence to a factorizable anti-pre-Novikov bialgebra.