论文标题
扭曲的Rota-baxter操作员和NS-Elgebras的同时和变形
Cohomology and deformations of twisted Rota-Baxter operators and NS-algebras
论文作者
论文摘要
本文的目的是双重的。在第一部分中，我们考虑了乌奇诺（Uchino）引入的联想代数的扭曲的旋转式运算符，作为扭曲泊松结构的非共同类似物。我们构建了一个$ l_ \ infty $ -Algebra，其Maurer-Cartan元素由Twisted Rota-Baxter操作员提供。这导致了与扭曲的rota-baxter操作员相关的共同体。该同胞可以将其视为特定联想代数的Hochschild共同体，并具有适当的双模模量的系数。我们通过上定义的共同体来研究扭曲的旋转式运算符的变形。申请给雷诺运营商。在第二部分中，我们认为Leroux的NS-Elgebras与扭曲的Rota-Baxter操作员相关的方式与Dendriform代数与Rota-Baxter Operators有关。我们使用乘法性作业来定义NS-Elgebras的共同体，并根据同种学研究其变形。
The aim of this paper is twofold. In the first part, we consider twisted Rota-Baxter operators on associative algebras that were introduced by Uchino as a noncommutative analogue of twisted Poisson structures. We construct an $L_\infty$-algebra whose Maurer-Cartan elements are given by twisted Rota-Baxter operators. This leads to cohomology associated to a twisted Rota-Baxter operator. This cohomology can be seen as the Hochschild cohomology of a certain associative algebra with coefficients in a suitable bimodule. We study deformations of twisted Rota-Baxter operators by means of the above-defined cohomology. Application is given to Reynolds operators. In the second part, we consider NS-algebras of Leroux that are related to twisted Rota-Baxter operators in the same way dendriform algebras are related to Rota-Baxter operators. We define cohomology of NS-algebras using multiplicative operads and study their deformations in terms of the cohomology.
