相关论文: Derivations and structure of the Lie algebras of X…
Generalising a previous work of Jiang and Sheng, a cohomology theory for differential Lie algebras of arbitrary weight is introduced. The underlying $L_\infty[1]$-structure on the cochain complex is also determined via a generalised version…
In this paper, we first introduce the concept of symmetric biderivation radicals and characteristic subalgebras of Lie algebras, and study their properties. Based on these results, we precisely determine biderivations of some Lie algebras…
Let $\mathbb{K}$ be a field, $R$ be an associative and commutative $\mathbb{K}$-algebra and $L$ be a Lie algebra over $\mathbb{K}$. We give some descriptions of injections from $L$ to Lie algebra of $\mathbb{K}$-derivations of $R$ in the…
Xu introduced a family of root-tree-diagram nilpotent Lie algebras of differential operators, in connection with evolution partial differential equations. We generalized his notion to more general oriented tree diagrams. These algebras are…
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…
In this paper, we determine the isomorphism classes of the central simple Poisson algebras introduced earlier by the second author. The Lie algebra structures of these Poisson algebras are in general not finitely-graded.
Classical contact Lie algebras are the fundamental algebraic structures on the manifolds of contact elements of configuration spaces in classical mechanics. In this paper, we determine the structure of the currently largest known category…
We consider the natural Lie algebra structure on the (associative) group algebra of a finite group $G$, and show that the Lie subalgebras associated to natural involutive antiautomorphisms of this group algebra are reductive ones. We give a…
In this paper, we introduce two new families of infinite-dimensional simple Lie algebras and a new family of infinite-dimensional simple Lie superalgebras. These algebras can be viewed as generalizations of the Block algebras.
We study classical R-matrices D for Lie algebras L such that D is also a derivation of L. This yields derivation double Lie algebras (L,D). The motivation comes from recent work on post-Lie algebra structures on pairs of Lie algebras…
This is a short survey on the recent developments made in the integration theory with effective formulas of algebraic structures stronger or higher than Lie algebras.
We show that formal isomorphism of intransitive linear Lie equations along transversal to the orbits can be extended to neighborhoods of these transversal. In analytic cases, the word formal is dropped from theorems. Also, we associate an…
After recalling the notion of Lie algebroid, we construct these structures associated with contact forms or systems. We are then interested in particular classes of Lie Rinehart algebras.
We give a full classification of Lie algebras of specific type in complexified Clifford algebras. These sixteen Lie algebras are direct sums of subspaces of quaternion types. We obtain isomorphisms between these Lie algebras and classical…
Derivations extend the concept of differentiation from functions to algebraic structures as linear operators satisfying the Leibniz rule. In Lie algebras, derivations form a Lie algebra via the commutator bracket of linear endomorphisms.…
The purpose of this paper is to study the structure and the algebraic varieties of Hom-associative algebras. We give characterize multiplicative simple Hom-associative algebras and show some examples deforming the $2\times 2$-matrix algebra…
The aim of this paper is to compare the structure and the cohomology spaces of Lie algebras and induced $3$-Lie algebras.
We describe automorphisms and derivations of several important associative and Lie algebras of infinite matrices over a field.
We classify the automorphic Lie algebras of equivariant maps from a complex torus to $\mathfrak{sl}_2(\mathbb{C})$. For each case we compute a basis in a normal form. The automorphic Lie algebras correspond precisely to two disjoint…
After briefly reviewing the methods that allow us to derive consistently new Lie (super)algebras from given ones, we consider enlarged superspaces and superalgebras, their relevance and some possible applications.