论文标题
反树枝状代数，新作战和Novikov类型代数
Anti-dendriform algebras, new splitting of operations and Novikov type algebras
论文作者
论文摘要
我们介绍了反树形代数的概念，作为分裂关联性的新方法。它们被描述为具有两个操作的代数，其总和是关联的，左右乘法算子组成了总和缔合代数的双模型，这证明了由于比较与树突状代数的相应表征而引起的概念。引入了抗 - $ \ $ \ Mathcal O $ $ $ $ $ $ $ $ $ $ $ \ the ofer-o $ $ $ $ $ $ $ $ $的概念，并引入了联想代数上的反rota-baxter操作员来解释抗树突状代数。特别是，与非排定交换的cocycles共同代数有兼容的抗树突状代数结构。有一个重要的观察结果，即树突状的某些子类和反树突形代数的对应关系在$ q $ - 代数方面。直接结果，我们将novikov型树突状代数的概念作为novikov代数代数的类似物代数，该代数代数代数代数，其与诺维科夫代数的关系与树突状和前代代数之间的诺维科夫代数相一致。最后，我们扩展了一个通用框架，以引入反树形形式代数的类似物的概念，该代数解释了新的操作分裂。
We introduce the notion of anti-dendriform algebras as a new approach of splitting the associativity. They are characterized as the algebras with two operations whose sum is associative and the negative left and right multiplication operators compose the bimodules of the sum associative algebras, justifying the notion due to the comparison with the corresponding characterization of dendriform algebras. The notions of anti-$\mathcal O$-operators and anti-Rota-Baxter operators on associative algebras are introduced to interpret anti-dendriform algebras. In particular, there are compatible anti-dendriform algebra structures on associative algebras with nondegenerate commutative Connes cocycles. There is an important observation that there are correspondences between certain subclasses of dendriform and anti-dendriform algebras in terms of $q$-algebras. As a direct consequence, we give the notion of Novikov-type dendriform algebras as an analogue of Novikov algebras for dendriform algebras, whose relationship with Novikov algebras is consistent with the one between dendriform and pre-Lie algebras. Finally we extend to provide a general framework of introducing the notions of analogues of anti-dendriform algebras, which interprets a new splitting of operations.
