Related papers: Semi-simple Leibniz algebras I
We present a new notion of non-positively curved groups: the collection of discrete countable groups acting (AU-)acylindrically on finite products of $\delta$-hyperbolic spaces with general type factors. Inspired by the classical theory of…
It is shown that any finite dimensional simple Lie superalgebra over an algebraically closed field of characteristic 0 is generated by 2 elements.
We describe non-trivial $\delta$-derivations of semisimple finite-dimensional Jordan algebras over an algebraically closed field of characteristic not 2, and of simple finite-dimensional Jordan superalgebras over an algebraically closed…
For a natural number $m$, a Lie algebra $L$ over a field $k$ is said to be of breadth type $(0, m)$ if the co-dimension of the centralizer of every non-central element is of dimension $m$. In this article, we classify finite dimensional…
We study maximal subalgebras of an arbitrary finite dimensional algebra over a field, and obtain full classification/description results of such algebras. This is done by first obtaining a complete classification in the semisimple case, and…
This paper is a sequel to our article [Feldvoss-Wagemann], where we mainly considered semi-simple Leibniz algebras. It turns out that the analogue of the Hochschild-Serre spectral sequence for Leibniz cohomology cannot be applied to many…
In this paper we focus on a certain self-distributive multiplication on coalgebras, which leads to so-called rack bialgebra. We construct canon-ical rack bialgebras (some kind of enveloping algebras) for any Leibniz algebra. Our motivation…
Lie algebras formed via semi-direct sums of the Witt algebra $\text{Der}(\mathbb{C}[t,t^{-1}])$ and its modules have become increasingly prominent in both physics and mathematics in recent years. In this paper, we complete the study of…
The main aim of this paper is to determine the multiplicative lie algebra structures on the semi-direct product of an abelian group with a group under certain conditions.
We continue the algebraic study of almost inner derivations of Lie algebras over a field of characteristic zero and determine these derivations for free nilpotent Lie algebras, for almost abelian Lie algebras, for Lie algebras whose…
The present paper is devoted to local and 2-local derivations and automorphism of complex finite-dimensional simple Leibniz algebras. We prove that all local derivations and 2-local derivations on a finite-dimensional complex simple Leibniz…
Given a symmetric Leibniz algebra $(\mathcal{L},.)$, the product is Lie-admissible and defines a Lie algebra bracket $[\;,\;]$ on $\mathcal{L}$. Let $G$ be the connected and simply-connected Lie group associated to $(\mathcal{L},[\;,\;])$.…
A discrete group which admits a faithful, finite dimensional, linear representation over a field $\mathbb F$ of characteristic zero is called linear. This note combines the natural structure of semi-direct products with work of A. Lubotzky…
Basing ourselves on the categorical notions of central extensions and commutators in the framework of semi-abelian categories relative to a Birkhoff subcategory, we study central extensions of Leibniz algebras with respect to the Birkhoff…
A subspace H of a Leibniz algebra L is called a quasi-ideal if [H;K] + [K;H] \subseteq H + K for every subspace K of L. They include ideals and subalgebras of codimension one in L. Quasi-ideals of Lie algebras were classified in two…
The aim of this paper is to provide an answer to the $\mathbb{C}[\partial]$-split extending structures problem for Leibniz conformal algebras, which asks that how to describe all Leibniz conformal algebra structures on $E=R\oplus Q$ up to…
We provide criteria for the cyclotomic quiver Hecke algebras of type C to be semisimple. In the semisimple case, we construct the irreducible modules.
We investigate the structure and representation theory of finite-dimensional $\mathbb{Z}$-graded Lie algebras, including the corresponding root systems and Verma, irreducible, and Harish-Chandra modules. This extends the familiar theory for…
In this article, we generalize Richardson's example of a rigid Lie algebra with non-trivial $H^2$ to the Leibniz setting. Namely, we consider the hemisemidirect product ${\mathfrak h}$ of a semidirect product Lie algebra…
We classify finite dimensional $H_{m^2}(\zeta)$-simple $H_{m^2}(\zeta)$-module Lie algebras $L$ over an algebraically closed field of characteristic $0$ where $H_{m^2}(\zeta)$ is the $m$th Taft algebra. As an application, we show that…