Related papers: Generalized Derivations of Lie triple systems

Let $k$ be an arbitrary field and $d$ a positive integer. For each degenerate symmetric or antisymmetric bilinear form $M$ on $k^{d}$ we determine the structure of the Lie algebra of matrices that preserve $M$, and of the Lie algebra of…

We introduce the notion of a generalized representation of a Jordan algebra with unit. The greneralized representation has the following properties: (1) Usual representations and Jacobson representations correspond to special cases of…

We study post-Lie algebra structures on pairs of Lie algebras (g,n), and prove existence results for the case that one of the Lie algebras is semisimple. For semisimple g and solvable n we show that there exist no post-Lie algebra…

In this note, we will prove that a finite dimensional Lie algebra $L$ of characteristic zero, admitting an abelian algebra of derivations $D\leq Der(L)$ with the property $$ L^n\subseteq \sum_{d\in D}d(L) $$ for some $n\geq 1$, is…

This paper primarily deals with the study of G-derivations associated with Lie-Yamaguti algebras. Taking G as an automorphism group, the concept of G-derivations, which is a derivation under both the bilinear and trilinear operations is…

We discuss the basic properties of Lie groupoids, Lie algebroids and Lie pseudo-groups in view of applying these techniques to the analysis of Jordan-H\"older resolutions and, subsequently, to the integration of partial differential…

The well-known Loday-Quillen-Tsygan theorem calculates the Lie algebra homology of the infinite general linear Lie algebra $\mathfrak{gl}(A)$ over an unital associative algebra $A$. We generalize the Loday-Quillen-Tsygan theorem to an…

In this paper, we introduce the concept and representation of modified $\lambda$-differential Lie triple systems. Next, we define the cohomology of modified $\lambda$-differential Lie triple systems with coefficients in a suitable…

This work explores the deformation theory of algebraic structures in a very general setting. These structures include commutative, associative algebras, Lie algebras, and the infinity versions of these structures, the strongly homotopy…

Twilled L(ie-)R(inehart)-algebras generalize, in the Lie-Rinehart context, complex structures on smooth manifolds. An almost complex manifold determines an "almost twilled pre-LR algebra", which is a true twilled LR-algebra iff the almost…

In this paper we provide some conditions under which a Lie derivation on a trivial extension algebra is proper, that is, it can be decomposed into the sum of a derivation and a center valued map. We extend some known results on the…

Let T be an algebraically bounded theory. We consider the $L(\bar\delta)$-expansions of T by a tuple $\bar \delta$ of derivations (which may be commuting or not). We investigate the model completion of either of the above theories, whose…

In this paper, we extend the concept of Lie superalgebras to a more generalized framework called Super-Lie superalgebras. In addition, they seem to be exploring various supergeneralizations of other algebraic structures, such as…

We introduce and study the triple of a quasitriangular Lie bialgebra as a natural extension of the Drinfeld double. The triple is itself a quasitriangular Lie bialgebra. We prove several results about the algebraic structure of the triple,…

This paper classifies the derivations of group algebras in terms of the generators and defining relations of the group. If $RG$ is a group ring, where $R$ is commutative and $S$ is a set of generators of $G$ then necessary and sufficient…

Highest weight categories arising in Lie theory are known to be associated with finite dimensional quasi-hereditary algebras such as Schur algebras or blocks of category $\mathcal O$. An analogue of the PBW theorem will be shown to hold for…

Let $\mathfrak{g}$ be a finite-dimensional complex Lie algebra and $\textrm{HLie}_{m}(\mathfrak{g})$ be the affine variety of all multiplicative Hom-Lie algebras on $\mathfrak{g}$. We use a method of computational ideal theory to describe…

A $G$-grading on a complex semisimple Lie algebra $L$, where $G$ is a finite abelian group, is called quasi-good if each homogeneous component is 1-dimensional and 0 is not in the support of the grading. Analogous to classical root systems,…

This paper lays the foundations for a nonlinear theory of differential geometry that is developed in a subsequent paper which is based on Colombeau algebras of tensor distributions on manifolds. We adopt a new approach and construct a…

We discuss a generalization of Clifford algebras known as generalized Clifford algebras (in particular, ternary Clifford algebras). In these objects, we have a fixed higher-degree form (in particular, a ternary form) instead of a quadratic…