Related papers: Generalized Derivations of Lie triple systems
The general theory of the radicals of Lie algebras are established. Baer radicals of untwisted affine Lie algebras are found.
The covariant derivative of the K\"ahler form of an almost pseudo-Hermitian or of an almost para-Hermitian manifold satisfies certain algebraic relations. We show, conversely, that any 3-tensor which satisfies these algebraic relations can…
Lie algebras are an important class of algebras which arise throughout mathematics and physics. We report on the formalisation of Lie algebras in Lean's Mathlib library. Although basic knowledge of Lie theory will benefit the reader, none…
We classify all the pairs of a commutative associative algebra with an identity element and its finite-dimensional commutative locally-finite derivation subalgebra such that the commutative associative algebra is derivation-simple with…
We extend the classical characterization of a finite-dimensional Lie algebra g in terms of its Maurer-Cartan algebra-the familiar differential graded algebra of alternating forms on g with values in the ground field, endowed with the…
A quasi-Lie scheme is a geometric structure that provides t-dependent changes of variables transforming members of an associated family of systems of first-order differential equations into members of the same family. In this note we…
A notion of an algebroid - a generalization of a Lie algebroid structure is introduced. We show that many objects of the differential calculus on a manifold M associated with the canonical Lie algebroid structure on T^M can be obtained in…
Relations between triple Jordan systems and integrable multi-component models of the modified Korteveg--de Vries type are established. The most general model is related to a pair consisting of a triple Jordan system and a skew-symmetric…
A previously introduced scheme for describing integrable deformations of of algebraic curves is completed. Lenard relations are used to characterize and classify these deformations in terms of hydrodynamic type systems. A general solution…
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…
We provide a complete classification of all algebras of generalised dihedral type, which are natural generalizations of algebras which occurred in the study of blocks with dihedral defect groups. This gives a description by quivers and…
An infinite-dimensional Lie Algebra is proposed which includes, in its subalgebras and limits, most Lie Algebras routinely utilized in physics. It relies on the finite oscillator Lie group, and appears applicable to twisted noncommutative…
We discuss a generalization of N=6 three-algebras to N=5 three-algebras in connection to anti-Lie triple systems and basic Lie superalgebras of type II. We then show that the structure constants defined in anti-Lie triple systems agree with…
We present a nonlinear realization of the 5-graded Lie algebra associated to a Kantor triple system. Any simple Lie algebra can be realized in this way, starting from an arbitrary 5-grading. In particular, we get a unified realization of…
We describe the ternary and the generalized superderivations of finite-dimensional semisimple Jordan superalgebras over an algebraically closed field of characteristic zero and of finite-dimensional simple Jordan superalgebras with…
Let $\mathbb{F}$ be a field of characteristic zero and let $\mathfrak{g}$ be a non-zero finite-dimensional split semisimple Lie algebra with root system $\Delta$. Let $\Gamma$ be a finite set of integral weights of $\mathfrak{g}$ containing…
The propose of this paper is to extend generalized representations of 3-Lie algebras to Hom-type algebras. We introduce the concept of generalized representation of multiplicative 3-Hom-Lie algebras, develop the corresponding cohomology…
We study the double derivation algebra $\mathcal{D}(\mathcal{L})$ of $n-$Hom Lie color algebra $\mathcal{L}$ and describe the relation between $\mathcal{D}(\mathcal{L})$ and the usual derivation Hom-Lie color algebra $Der(\mathcal{L}).$ We…
If one wishes to define a complete Leibniz algebra in such a way as to extend the notion of a complete Lie algebra, two distinct definitions can be found in the current literature. Since biderivations on complete Lie algebras have already…
The theory of Lie systems has recently been applied to Quantum Mechanics and additionally some integrability conditions for Lie systems of differential equations have also recently been analysed from a geometric perspective. In this paper…