The main object of study of this paper is the notion of a Lie Der pair, ie a Lie algebra with a
derivation. We introduce the concept of a representation of a Lie Der pair and study the …

Abstract A Rota-Baxter Lie algebra g T is a Lie algebra g equipped with a Rota-Baxter
operator T: g→ g. In this paper, we consider non-abelian extensions of a Rota-Baxter Lie …

Lie-Yamaguti algebras generalize both the notions of Lie algebras and Lie triple systems. In
this paper, we consider the inducibility problem for automorphisms of Lie-Yamaguti algebra …

In this paper, we first show that there is a Hom-Lie algebra structure on the set of (σ, σ)-
derivations of an associative algebra. Then we construct the dual representation of a …

In this paper, we introduce the notions of crossed module of associative conformal algebras,
2-term strongly homotopy associative conformal algebras, and discuss the relationship …

The purpose of the present paper is to study cohomologies and non-abelian extensions of λ-
differential pre-Lie algebras. First, we consider representations and cohomologies of λ …

In this paper, we introduce two-term differential L eib∞-conformal algebras and give
characterizations of some particular classes of such two-term differential L eib∞-conformal …

A Rota-Baxter algebra $ A_R $ is an algebra $ A $ equipped with a distinguished Rota-
Baxter operator $ R $ on it. Rota-Baxter algebras are closely related to dendriform algebras …

Abelian extensions of Lie triple systems with derivations Page 1 http://www.aimspress.com/journal/era
ERA, 30(3): 1087–1103. DOI: 10.3934/era.2022058 Received: 22 July 2021 Revised: 29 …

In recent years, averaging operators on Lie algebras (also called embedding tensors in the
physics literature) and associated tensor hierarchies have formed an efficient tool for …