相关论文: Do $n$-Lie algebras have universal enveloping alge…

For n even, we prove Pozhidaev's conjecture on the existence of associative enveloping algebras for simple n-Lie algebras. More generally, for n even and any (n+1)-dimensional n-Lie algebra L, we construct a universal associative enveloping…

In this paper we generalize classical results on Lie algebras and universal enveloping algebras of Lie algebras to Lie-Rinehart algebras. We define for any Lie-Rinehart algebra $L$ and any cocycle $f$ in $Z^2(L,B)$, a universal enveloping…

We prove how the universal enveloping algebra constructions for Lie-Rinehart algebras and anchored Lie algebras are naturally left adjoint functors. This provides a conceptual motivation for the universal properties these constructions…

Lie antialgebras is a class of supercommutative algebras recently appeared in symplectic geometry. We define the notion of enveloping algebra of a Lie antialgebra and study its properties. We show that every Lie antialgebra is canonically…

A cohomology theory, associated to a $n$-Lie algebra and a representation space of it, is introduced. It is observed that this cohomology theory is qualified to encode the generalized derivation extensions, and that it coincides, for $n=3$,…

Given a finite dimensional Lie algebra $L$ let $I$ be the augmentation ideal in the universal enveloping algebra $U(L)$. We study the conditions on $L$ under which the $Ext$-groups $Ext (k,k)$ for the trivial $L$-module $k$ are the same…

In this dissertation, we investigate the cohomology theory of restricted Lie algebras. The representation theory of restricted Lie algebras is reviewed including a description of the restricted universal enveloping algebra. In the case of…

In this note we point out that the definition of the universal enveloping dialgebra for a Leibniz algebra is consistent with the interpretation of a Leibniz algebra as a generalization not of a Lie algebra, but of the adjoint representation…

The purpose of this paper is to investigate $(n+1)$-Lie algebras induced by $n$-Lie algebras and trace maps. We highlight a comparison of their structure properties (solvability, nilpotency) and the cohomology groups as well as central…

The purpose of this paper is to discuss the universal algebra theory of hom-algebras. This kind of algebra involves a linear map which twists the usual identities. We focus on hom-associative algebras and hom-Lie algebras for which we…

Let $\mathfrak{g}$ and $\mathfrak{h}$ be two Lie algebras with $\mathfrak{h}$ finite dimensional and consider ${\mathcal A} = {\mathcal A} (\mathfrak{h}, \, \mathfrak{g})$ to be the corresponding universal algebra as introduced in…

We explicitly compute the first and second cohomology groups of the classical Lie superalgebras $sl_{m|n}$ and $osp_{2|2n}$ with coefficients in the finite dimensional irreducible modules and the Kac modules. We also show that the second…

In this paper we study the isomorphism problem for the universal enveloping algebras of nilpotent Lie algebras. We prove that if the characteristic of the underlying field is not~2 or~3, then the isomorphism type of a nilpotent Lie algebra…

We construct the universal enveloping algebra of a Hom-Lie algebra and endow it with a Hom-Hopf algebra structure. We discuss group-like elements that we see as a Hom-group integrating the initial Hom-Lie algebra.

The present paper can be thought of as a continuation of the paper "Introduction to sh Lie algebras for physicists" by T. Lada and J. Stasheff (International Journal of Theoretical Physics Vol. 32, No. 7 (1993), 1087--1103, appeared also as…

Absolute algebras are a new type of algebraic structures, endowed with a meaningful notion of infinite sums of operations without supposing any underlying topology. Opposite to the usual definition of operadic calculus, they are defined as…

The aim of this note is to prove various general properties of a generalization of the full module of first order differential operators on a commutative ring - a $\operatorname{D}$-Lie algebra. A $\operatorname{D}$-Lie algebra $\tilde{L}$…

The universal enveloping algebra $\mathscr{U}$ of a two-dimensional nonabelian Lie algebra $L$ is a Lie algebra itself with the commutator as Lie bracket. There exists a presentation of $\mathscr{U}$ with generators $x,y$ and relation…

Let $G$ be an abelien group, $\epsilon$ an anti-bicharacter of $G$ and $L$ a $G$-graded $\epsilon$ Lie algebra (color Lie algebra) over $\K$ a field of characteristic zero. We prove that all $G$-graded, positive filtered $A$ such that the…

We introduce a notion of $n$-Lie Rinehart algebras as a generalization of Lie Rinehart algebras to $n$-ary case. This notion is also an algebraic analogue of $n$-Lie algebroids. We develop representation theory and describe a cohomology…