Related papers: On simple $15$-dimensional Lie algebras in charact…
In this paper, we classify (n+5)-dimensional nilpotent n-Lie algebras of class two over the arbitrary field, when $n\ge 3$.
The paper aims to investigate the classification problem of low dimensional complex none Lie filiform Leibniz algebras. There are two sources to get classification of filiform Leibniz algebras. The first of them is the naturally graded none…
This is a survey of the existing literature, the state of the art, and a few minor new results and open questions regarding the essential dimension of central simple algebras and finite sequences of such algebras over fields whose…
Inner ideals of simple locally finite dimensional Lie algebras over an algebraically closed field of characteristic 0 are described. In particular, it is shown that a simple locally finite dimensional Lie algebra has a non-zero proper inner…
A Lie superalgebra is attached to any finite-dimensional J-ternary algebra over an algebraically closed field of characteristic 3, using a process of semisimplification via tensor categories. Some of the exceptional simple Lie algebras,…
We compute the restricted infinitesimal deformations of the restricted simple Lie algebras over an algebraically closed field of characteristic different from 2 and 3.
We investigate restricted Lie algebras arising as analogues of (twisted) right-angled Artin groups and right-angled Coxeter groups over fields of characteristic two. These algebras are defined via quadratic relations determined by decorated…
In the present paper we present a classification of Lie bialgebra structures on Lie algebras of type g[[u]] and g[u], where g is a simple finite dimensional Lie algebra.
A finite dimensional filiform K-Lie algebra is a nilpotent Lie algebra g whose nil index is maximal, that is equal to dim g -1. We describe necessary and sufficient conditions for a filiform algebra over an algebraically closed field of…
The aim of this paper is to extend the theory of standard subalgebras of finite dimensional simple Lie algebras to infinite dimensional Lie algebras. We construct and characterize a class of standard subalgebras of affine Kac-Moody algebra.
The fine abelian group gradings on the simple exceptional classical Lie superalgebras over algebraically closed fields of characteristic 0 are determined up to equivalence.
As is well-known, the dimension of the space spanned by the non-degenerate invariant symmetric bilinear forms (NISes) on any simple finite-dimensional Lie algebra or Lie superalgebra is equal to at most 1 if the characteristic of the…
This paper is devoted to the description of complex finite-dimensional algebras of level two. We obtain the classification of algebras of level two in the varieties of Jordan, Lie and associative algebras.
We give a simplified complete proof for the classification of the selfinjective representation-finite algebras of finite dimension over an algebraically closed field. We explain the relations between the two different approaches and also to…
This paper is a contribution to the isomorphism problem for universal enveloping algebras of finite-dimensional Lie algebras. We focus on solvable Lie algebras of small dimensions over fields of arbitrary characteristic. We prove, over an…
Nongraded infinite-dimensional Lie algebras appeared naturally in the theory of Hamiltonian operators, the theory of vertex algebras and their multi-variable analogues. They play important roles in mathematical physics. This survey article…
We construct four new series of generalized simple Lie algebras of Cartan type, using the mixtures of grading operators and down-grading operators. Our results in this paper are further generalizations of those in Osborn's work ``New simple…
For sufficiently high dimensions, the naturally graded nonsplit nilpotent Lie algebras with linear characteristic sequence are classified.
$F-$Lie algebras are natural generalisations of Lie algebras (F=1) and Lie superalgebras (F=2). When $F>2$ not many finite-dimensional examples are known. In this paper we construct finite-dimensional $F-$Lie algebras $F>2$ by an inductive…
We determine all two-dimensional Lie subalgebras of the centreless Virasoro algebra and complete the characterization of all finite dimensional Lie subalgebras of the complex Virasoro algebra.