Related papers: Lie and Jordan products in interchange algebras

Velasquez and Felipe recently introduced quasi-Jordan algebras based on the product $a \triangleleft b = \tfrac12 ( a \dashv b + b \vdash a )$ in an associative dialgebra with operations $\dashv$ and $\vdash$. We determine the polynomial…

We classify, up to isomorphism, the 2-dimensional algebras over a field K. We focuse also on the case of characteristic 2, identifying the matrices of GL(2,F_2) with the elements of the symmetric group S_3. The classification is then given…

We study polynomial identities satisfied by the mutation product $xpy - yqx$ on the underlying vector space of an associative algebra $A$, where $p, q$ are fixed elements of $A$. We simplify known results for identities in degree $4$,…

The classification, up to isomorphism, of two-dimensional (not necessarily commutative) Jordan algebras over algebraically closed fields and $\mathbb{R}$ is presented in terms of their matrices of structure constants.

In this paper we explore the Lie enveloping algebra of a post-Lie algebra derived from a classical $R$-matrix. An explicit exponential solution of the corresponding Lie bracket flow is presented. It is based on the solution of a post-Lie…

We look at the Poisson structure on the total space of the dual bundle to the Lie algebroid arising from a matched pair of Lie groups. This dual bundle, with the natural semidirect product group structure, becomes a Poisson-Lie group as…

We show that there is an equivalence of $\infty$-categories between Lie algebroids and certain kinds of curved Lie algebras. For this we develop a method to study the $\infty$-category of curved Lie algebras using the homotopy theory of…

Let g be a simple Lie algebra of rank n over C. We show that the n-dimensional abelian ideals of a Borel subalgebra of g are limits of Jordan Lie subalgebras. Combining this with a classical result by Kostant, we show that the g-module…

We continue the study undertaken in \cite{DV} of the exceptional Jordan algebra $J = J_3^8$ as (part of) the finite-dimensional quantum algebra in an almost classical space-time approach to particle physics. Along with reviewing known…

We prove a discretized sum-product theorem for representations of Lie groups whose Jordan-H\"older decomposition does not contain the trivial representation. This expansion result is used to derive a product theorem in perfect Lie groups.

In this article we prove that the elliptic, hyperbolic and nilpotent (or unipotent) additive (or multiplicative) Jordan components of an endomorphism $X$ (or an isomorphism $g$) of a finite dimensional vector space are given by polynomials…

We study surjective homomorphisms f:\prod_I A_i\to B of not-necessarily-associative algebras over a commutative ring k, for I a generally infinite set; especially when k is a field and B is countable-dimensional over k. Our results have the…

We describe Hom-Lie structures on affine Kac-Moody and related Lie algebras, and discuss the question when they form a Jordan algebra.

Lie algebras endowed with an action by automorphisms of any of the symmetric groups S3 or S4 are considered, and their decomposition into a direct sum of irreducible modules for the given action is studied. In case of S3-symmetry, the Lie…

Let $\mathbb{K}$ be a field of characteristic different from $2$, and let $M_n(\mathbb{K})$ be the algebra of all $n\times n$ matrices over $\mathbb{K}$. We consider the corresponding special Jordan algebra $\mathcal{A}:=M_n(\mathbb{K})^+$…

Decomposition classes provide a way of partitioning the Lie algebras of an algebraic group into equivalence classes based on the Jordan decomposition. In this paper, we investigate the decomposition classes of the Lie algebras of connected…

We generalize the common notion of descending and ascending central series. The descending approach determines a naturally graded Lie ring and the ascending version determines a graded module for this ring. We also link derivations of these…

We construct two superalgebras associated to a punctured Riemann surface. One of them is a Lie superalgebra of Krichever-Novikov type, the other one is a Jordan superalgebra. The constructed algebras are related in several ways (algebraic,…

In this work we generalize the concept of product by generators to the class of solvable Lie algebras. We analyze the number of invariants by the coadjoint representation by means of Maurer-Cartan equations and give some applications to…

The simple 7-dimensional Malcev algebra $M$ is isomorphic to the irreducible $\mathfrak{sl}(2,\mathbb{C})$-module V(6) with binary product $[x,y] = \alpha(x \wedge y)$ defined by the $\mathfrak{sl}(2,\mathbb{C})$-module morphism…