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 non-symmetric operads and study their deformations in terms of the cohomology.

本文的目的是双重的。在第一部分中，我们考虑关联代数上的扭曲 Rota-Baxter 算子，该算子由 Uchino 引入，作为扭曲泊松结构的非交换模拟。我们构造一个\(L_\infty \)代数，其 Maurer-Cartan 元素由扭曲的 Rota-Baxter 算子给出。这导致与扭曲的 Rota-Baxter 算子相关的上同调。这种上同调可以看作是某个关联代数与适当双模中的系数的 Hochschild 上同调。我们通过上述定义的上同调研究扭曲 Rota-Baxter 算子的变形。申请已提交给雷诺操作员。在第二部分中，我们考虑与扭曲 Rota-Baxter 算子相关的 Leroux NS 代数，就像树状代数与 Rota-Baxter 算子相关一样。我们使用非对称操作数定义 NS 代数的上同调，并根据上同调研究它们的变形。