Deformation quantization, which gives a development of quantum mechanics independent
of the operator algebra formulation, and quantum groups, which arose from the inverse …

We use the concept of gauge transformations of quasi-Hopf algebras to study twists of
algebraic structures based on actions of a bialgebra and relate this to the theory of universal …

In this paper, we introduce the concept and representation of modified $\lambda $-
differential Lie triple systems. Next, we define the cohomology of modified $\lambda …

The purpose of the present paper is to investigate cohomologies of relative Rota-Baxter Lie
algebras with derivations and applications. First, we introduce a notion of relative Rota …

The goal of this paper is to study cohomological theory of n-Lie algebras with derivations.
We define the representation of an n-LieDer pair and consider its cohomology. Likewise, we …

In this paper, we use the higher derived bracket to give the controlling algebra of pre-LieDer
pairs. We give the cohomology of pre-LieDer pairs by using the twist $ L_\infty $-algebra of …

In this paper we lay the foundation for studying quantum groups as part of algebraic
deformation theory by introducing the quantum symmetric group and the concept of quantum …

In this paper, we introduce the notion of a LeibtsDer pair, ie, a Leibniz triple system with a
derivation. We define a representation of a LeibtsDer pair and the corresponding …

We study formal deformations of multiplication in an operad. This closely resembles
Gerstenhaber's deformation theory for associative algebras. However, this applies to various …

In this paper, first, we introduce a notion of modified Rota-Baxter Lie algebras of weight
$\mathrm {\lambda} $ with derivations (or simply modified Rota-Baxter LieDer pairs) and …