Related papers: On (n+2)-dimensional n-Lie algebras

We provide a clarification of the classification of two-dimensional algebras over an arbitrary base field. Using this clarification, we determine the number of non-isomorphic two-dimensional algebras over a finite field.

We study $\mathbb{Z}_2$-graded identities of Lie superalgebras of the type $b(t), t\ge 2$, over a field of characteristic zero. Our main result is that the $n$-th codimension is strictly less than $(\dim b(t))^n$ asymptotically. As a…

In this paper, we develop a method to obtain the algebraic classification of compatible pre-Lie algebras from the classification of pre-Lie algebras of the same dimension. We use this method to obtain the algebraic classification of complex…

Brief proofs of classical results of Lie on finite dimensional subalgebras of vector fields in two and three variables are outlined. The results for algebras of maximal rank for vector fields in $\mathbb{C}^N$ -- $N$ arbitrary -- are also…

A commutative Poisson subalgebra of the Poisson algebra of polynomials on the Lie algebra of n x n matrices over ${\Bbb C}$ is introduced which is the Poisson analogue of the Gelfand-Zeitlin subalgebra of the universal enveloping algebra.…

3-Lie algebras have close relationships with many important fields in mathematics and mathematical physics. The paper concerns 3-Lie algebras. The concepts of 3-Lie coalgebras and 3-Lie bialgebras are given. The structures of such…

We initiate the representation theory of restricted Lie superalgebras over an algebraically closed field of characteristic p>2. A superalgebra generalization of the celebrated Kac-Weisfeiler Conjecture is formulated, which exhibits a…

Let $K$ be an algebraically closed field of characteristic zero, $A= K[x_1, \dots, x_n]$ the polynomial ring in $n$ variables, and let $W_n(K)$ be the Lie algebra of all $K$-derivations of $A.$ This Lie algebra also is the free $A$-module…

Using techniques developed in a recent article by the authors, it is proved that the 2-cohomology of the Lie superalgebra sl(m|1); m > 1, with coefficients in its enveloping algebra is trivial. The obstacles in solving the analogous problem…

The indecomposable solvable Lie algebras with graded nilradical of maximal nilindex and a Heisenberg subalgebra of codimension one are analyzed, and their generalized Casimir invariants calculated. It is shown that rank one solvable…

We determine the maximal dimension of totally geodesic subalgebras of N-graded filiform Lie algebras, and we show that these bounds are attained.

In this work, we consider Lie algebras L containing a subalgebra isomorphic to sl3 and such that L decomposes as a module for that sl3 subalgebra into copies of the adjoint module, the natural 3-dimensional module and its dual, and the…

We classify all complex $7$- and $8$-dimensional dual mock-Lie algebras by algebraic and geometric way. Also we find all non-trivial complex $9$-dimensional dual mock-Lie algebras.

There are some results on nilpotent Lie algebras $ L $ investigate the structure of $ L $ rely on the study of its $2$-nilpotent multiplier. It is showed that the dimension of the $2$-nilpotent multiplier of $ L $ is equal to $ \frac{1}{3}…

For a Lie ring $L$ over the ring of integers, we compare its lower central series $\{\gamma_n(L)\}_{n\geq 1}$ and its dimension series $\{\delta_n(L)\}_{n\geq 1}$ defined by setting $\delta_n(L)= L\cap \varpi^n(L)$, where $\varpi(L)$ is the…

An algorithm for embedding finite dimensional Lie algebras into Lie algebras of vector fields (and Lie superalgebras into Lie superalgebras of vector fields) is offered in a way applicable over ground fields of any characteristic. The…

This paper investigates cohomology and support varieties for Lie superalgebras and restricted Lie superalgebras over a field of characteristic 2. The existence of an underlying ordinary Lie algebra allows us to obtain results that are still…

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…

We study codimension growth of infinite dimensional Lie superalgebras over an algebraically closed field of characteristic zero. We prove that if a Lie superalgebra $L$ is a Grassmann envelope of a finite dimensional simple Lie algebra then…

A result of Barnea and Isaacs states that if $L$ is a finite dimensional nilpotent Lie algebra with exactly two distinct centralizer dimensions, then nilpotency class of $L$ is either $2$ or $3$. In this article, we classify all such finite…