Related papers: Commutative post-Lie algebra structures on Lie alg…

We consider the group algebra of the symmetric group as a superalgebra, and describe its Lie subsuperalgebra generated by the transpositions. The updated version corrects some of the arguments made in Sections 4.5 - 4.7. The statements of…

We study a new class of infinite dimensional Lie algebras, which has important applications to the theory of integrable equations. The construction of these algebras is very similar to the one for automorphic functions and this motivates…

It is pointed out that affine Lie algebras appear to be the natural mathematical structure underlying the notion of integrability for two-dimensional systems. Their role in the construction and classification of 2D integrable systems is…

We introduce the notion of omni-Lie 2-algebra, which is a categorification of Weinstein's omni-Lie algebras. We prove that there is a one-to-one correspondence between strict Lie 2-algebra structures on 2-sub-vector spaces of a 2-vector…

We describe a class (called regular) of invariant generalized complex structures on a real semisimple Lie group G. The problem reduces to the description of admissible pairs (\gk, \omega), where \gk is an appropriate regular subalgebra of…

We introduce the notion of a conformal pseudo-subriemannian fundamental graded Lie algebra of semisimple type. Moreover we give a classification of conformal pseudo-subriemannian fundamental graded Lie algebras of semisimple type and their…

This paper contains an elementary proof of the existence of the classical model structure on the category of unbounded DG-Lie algebras over a field of characteristic zero, with an emphasis on the properties of free and semifree extensions,…

Let $\mathcal A$ be a Banach algebra for which the group of invertible elements is connected. A subspace $\mathcal L \subseteq \mathcal A$ is a Lie ideal in $\mathcal A$ if, and only if, it is invariant under inner automorphisms. This…

We construct a convenient basis for all real semisimple Lie algebras by means of an adapted Chevalley basis of the complexification. It determines rational and in fact half-integer structure constants which we express only in terms of the…

In this article, we described 1/2-derivations of solvable Lie algebras with a thread-like nilradical. Nontrivial transposed Poisson algebras with solvable Lie algebras are constructed. That is, by using 1/2-derivations of Lie algebras, we…

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…

Over a field $F$ of any characteristic, for a commutative associative algebra $A$ with an identity element and for the polynomial algebra $F[D]$ of a commutative derivation subalgebra $D$ of $A$, the associative and the Lie algebras of Weyl…

The aim of this paper is to introduce the notion of (noncommutative) transposed Poisson conformal algebras, which serve as the conformal analogues of transposed Poisson algebras and admit a rich class of identities. We show that the tensor…

Applying Groebner-Shirshov technique, we prove that any post-Lie algebra injectively embeds into its universal enveloping postassociative algebra.

We introduce the notion of $\lambda$-double Lie algebra, which coincides with usual double Lie algebra when $\lambda = 0$. We state that every $\lambda$-double Lie algebra for $\lambda\neq0$ provides the structure of modified double Poisson…

We prove conditions ensuring that a Lie ideal or an invariant additive subgroup in a ring contains all additive commutators. A crucial assumption is that the subgroup is fully noncentral, that is, its image in every quotient is noncentral.…

We obtain structure results for locally conformally symplectic Lie algebras. We classify locally conformally symplectic structures on four-dimensional Lie algebras and construct locally conformally symplectic structures on compact quotients…

We consider the Casimir Invariants related to some a special kind of Lie-algebra extensions, called universal extensions. We show that these invariants can be studied using the equivalence between the universal extensions and the…

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…

A new kind of graded Lie algebra (we call it $Z_{2,2}$ graded Lie algebra) is introduced as a framework for formulating parasupersymmetric theories. By choosing suitable bose subspace of the $Z_{2,2}$ graded Lie algebra and using relevant…