In this paper, we give Maurer-Cartan characterizations as well as a cohomology theory for
compatible Lie algebras. Explicitly, we first introduce the notion of a bidifferential graded Lie …

In this paper, we first construct the controlling algebras of embedding tensors and Lie–
Leibniz triples, which turn out to be a graded Lie algebra and an L_ ∞ L∞-algebra …

A relative Rota–Baxter algebra is a triple (A, M, T) consisting of an algebra A, an A-bimodule
M, and a relative Rota–Baxter operator T. Using Voronov's derived bracket and a recent …

In this paper, we first construct a differential graded Lie algebra that controls deformations of
a Lie-Yamaguti algebra. Furthermore, a relative Rota-Baxter operator on a Lie-Yamaguti …

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 …

In this paper, first we give the notion of a compatible 3-Lie algebra and construct a
bidifferential graded Lie algebra whose Maurer-Cartan elements are compatible 3-Lie …

In this paper, we consider compatible Hom-Leibniz algebra where the Hom map twists the
operations in the compatible system. We consider a suitably graded Lie algebra whose …

We give a general treatment of deformation theory from the point of view of homotopical
algebra following Hinich, Manetti and Pridham. In particular, we show that any deformation …

In this paper we study a cohomology theory of compatible Leibniz algebra. We construct a
graded Lie algebra whose Maurer-Cartan elements characterize the structure of compatible …

The purpose of the present paper is to study representations and cohomologies of
differential 3-Lie algebras with any weight. We introduce the representation of a differential 3 …