论文标题
相对旋转式代数和共同体上的双模型
Bimodules over relative Rota-Baxter algebras and cohomologies
论文作者
论文摘要
相对Rota-Baxter代数是Rota-Baxter代数的概括。相对Rota-baxter代数与树突形代数密切相关。在本文中，我们在相对的旋转式代数上引入双模型，该代数与树突状代数的表示。我们定义了双模块中具有系数的相对Rota-baxter代数的共同体，然后根据第二个共同体学组研究相对Rota-Baxter代数的Abelian扩展。最后，我们考虑了同型相对rota-baxter代数，并根据上定义的共同体学对骨骼同义相对rota-baxter代数进行了分类。
A relative Rota-Baxter algebra is a generalization of a Rota-Baxter algebra. Relative Rota-Baxter algebras are closely related to dendriform algebras. In this paper, we introduce bimodules over a relative Rota-Baxter algebra that fits with the representations of dendriform algebras. We define the cohomology of a relative Rota-Baxter algebra with coefficients in a bimodule and then study abelian extensions of relative Rota-Baxter algebras in terms of the second cohomology group. Finally, we consider homotopy relative Rota-Baxter algebras and classify skeletal homotopy relative Rota-Baxter algebras in terms of the above-defined cohomology.
