Related papers: On index of certain nilpotent Lie algebras

Following the structure theory approach for rings, the aim of this paper is to study some distinguished classes of Lie algebras. We introduce the notion of a Lie-module and discuss some relations of it with various classes of ideals of a…

We determine the Lie superalgebras that are graded by the root systems of the basic classical simple Lie superalgebras of type A$(m,n)$.

A brief proof of Lie's classification of solvable algebras of vector fields on the plane is given. The proof uses basic representation theory and PDEs.

In this article, we introduce the concepts of excision and idealization for a multiplicative Lie algebra (also for a Lie algebra), which provides two new multiplicative Lie algebras (or Lie algebras) from a given multiplicative Lie algebra…

Let $M$ be a maximal subalgebra of a Lie algebra $L$ and $A/B$ a chief factor of $L$ such that $B \subseteq M$ and $A \not \subseteq M$. We call the factor algebra $M \cap A/B$ a $c$-section of $M$. All such $c$-sections are isomorphic, and…

We define covariant Lie derivatives acting on vector-valued forms on Lie algebroids and study their properties. This allows us to obtain a concise formula for the Fr\"olicher-Nijenhuis bracket on Lie algebroids.

In this work, we extend the definition of the graded prime ideals from those in commutative graded rings to the ideals over graded Lie algebras. We prove some facts about graded prime Lie ideals in arbitrary Lie algebras that are similar to…

The space of vector-valued forms on any manifold is a graded Lie algebra with respect to the Frolicher-Nijenhuis bracket. In this paper we consider multiplicative vector-valued forms on Lie groupoids and show that they naturally form a…

Let $K$ be an arbitrary field of characteristic zero and $A$ a commutative associative $ K$-algebra which is an integral domain. Denote by $R$ the fraction field of $A$ and by $W(A)=RDer_{\mathbb K}A,$ the Lie algebra of $\mathbb…

We generalize the Schouten calculus of multivector fields to commutative Lie Rinehart pairs and define a non negatively graded Lie oo-algebra on their exterior power.

We construct representation theory of Lie algebras with filtrations. In this framework a classification of irreducible representations is obtained and spectra of some reducible representations are found.

A (vector space) basis B of a Lie algebra is said to be very nilpotent if all the iterated brackets of elements of B are nilpotent. In this note, we prove a refinement of Engel's Theorem. We show that a Lie algebra has a very nilpotent…

We classify irreducible finite-dimensional modules of a collection of real Lie superalgebras that includes the simple ones, their classical variants, complex Lie superalgebras after restriction of scalars, and all real Lie algebras. Our…

We present an explicit description of the affine variety of Lie algebras of the maximal class (filiform Lie algebras): the formulas of polynomial equations that determine this variety are written. It can considered as the base of the…

We study almost inner derivations of Lie algebras, which were introduced by Gordon and Wilson in their work on isospectral deformations of compact solvmanifolds. We compute all almost inner derivations for low-dimensional Lie algebras, and…

For each complex 8-dimensional filiform Lie algebra we find another non isomorphic Lie algebra that degenerates to it. Since this is already known for nilpotent Lie algebras of rank $\ge 1$, only the caracteristically nilpotent ones should…

The index of a Lie algebra is an important algebraic invariant. In 2000, Vladimir Dergachev and Alexandre Kirillov defined seaweed subalgebras of $\mathfrak{gl}_n$ (or $\mathfrak{sl}_n$) and provided a formula for the index of a seaweed…

We study the possibility of factoring a covariant distribution on reductive Lie algebras as finite sum of products of an invariant distribution by a covariant polynomial.

In this paper we present new formulas, which represent commutators and anticommutators of Clifford algebra elements as sums of elements of different ranks. Using these formulas we consider subalgebras of Lie algebras of pseudounitary…

A family of Lie algebras of minimal dimension associated with vector fields that define a non-linear dynamical system is calculated. These Lie algebras contain the Heinsenberg algebra. An element that distinguishes these vector fields is…