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 …

The second cohomology group of a left skew brace with coefficients in a trivial left brace with
non-trivial actions is defined, its connection with extensions of a left skew brace by a trivial …

Let 0→ A→ L→ B→ 0 be a short exact sequence of Lie algebras over a field F, where A is
abelian. We show that the obstruction for a pair of automorphisms in Aut (A)× Aut (B) to be …

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 …

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 …

Let 0→ a→ e→ g→ 0 be an abelian extension of Lie superalgebras. In this article,
corresponding to this extension we construct two exact sequences connecting the various …

In mathematics, the theory of groups is a basic tool for the study of symmetries of objects.
From this point of view, the symmetries of a group G itself are encoded in the automorphism …