论文标题
广义的旋转式系统
Generalized Rota-Baxter systems
论文作者
论文摘要
T.brzeziński的Rota-baxter系统是与树突状结构，关联的杨 - 巴克斯特对和协变量的双ggebras相关的Rota-baxter操作员的概括。在本文中，我们考虑了在Bimodule存在下的Rota-Baxter系统，我们称之为广义的Rota-Baxter系统。我们定义了一个分级的谎言代数，其毛勒 - 卡丹元素是概括性的rota-baxter系统。这使我们能够为广义的旋转式 - 巴克斯特系统定义一个共同体学理论。从共同体的角度讨论了广义旋转式系统系统的形式的一参数变形。我们进一步研究Rota-baxter系统，联想的杨 - 巴克斯特对，协变量的双gebras，并引入了与关联拨号桥相关的广义平均系统。接下来，我们在同型上下文中定义了广义的旋转式系统，并找到与同型树突状代数的关系。该论文以考虑通勤旋转式系统及其与四边形代数的关系结束。
Rota-Baxter systems of T. Brzeziński are a generalization of Rota-Baxter operators that are related to dendriform structures, associative Yang-Baxter pairs and covariant bialgebras. In this paper, we consider Rota-Baxter systems in the presence of bimodule, which we call generalized Rota-Baxter systems. We define a graded Lie algebra whose Maurer-Cartan elements are generalized Rota-Baxter systems. This allows us to define a cohomology theory for a generalized Rota-Baxter system. Formal one-parameter deformations of generalized Rota-Baxter systems are discussed from cohomological points of view. We further study Rota-Baxter systems, associative Yang-Baxter pairs, covariant bialgebras and introduce generalized averaging systems that are related to associative dialgebras. Next, we define generalized Rota-Baxter systems in the homotopy context and find relations with homotopy dendriform algebras. The paper ends by considering commuting Rota-Baxter systems and their relation with quadri-algebras.
