Related papers: Jordanable almost Abelian Lie algebras

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…

Results on derivations and automorphisms of some quantum and classical Poisson algebras, as well as characterizations of manifolds by the Lie structure of such algebras, are revisited and extended. We prove in particular somehow unexpected…

We investigate linear operators between C$^\ast$-algebras which approximately preserve involution and orthogonality, the latter meaning that for some $\varepsilon>0$ we have $\|\phi(x)\phi(y)\|\leq\varepsilon\|x\|\|y\|$ for all positive…

A nilpotent Lie algebra n_{n,1} with an (n-1) dimensional Abelian ideal is studied. All indecomposable solvable Lie algebras with n_{n,1} as their nilradical are obtained. Their dimension is at most n+2. The generalized Casimir invariants…

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…

We define the notion of an almost polynomial identity of an associative algebra $R$, and show that its existence implies the existence of an actual polynomial identity of $R$. A similar result is also obtained for Lie algebras and Jordan…

We show that a primitive axial algebra of Jordan type $\eta = \tfrac{1}{2}$ is a Jordan algebra if and only if every $2$-generated subalgebra is \emph{solid}, a notion introduced recently by Ilya Gorshkov, Sergey Shpectorov and Alexei…

We first establish some general results connecting real and complex Lie algebras of first-order differential operators. These are applied to completely classify all finite-dimensional real Lie algebras of first-order differential operators…

We propose a systematic procedure to construct polynomial algebras from intermediate Casimir invariants arising from (semisimple or non-semisimple) Lie algebras $\mathfrak{g}$. In this approach, we deal with explicit polynomials in the…

We study finite-dimensional commutative algebras, which satisfy the Jacobi identity. Such algebras are Jordan algebras. We describe some of their properties and give a classification in dimensions $n<7$ over algebraically closed fields of…

We associate Hamiltonian homological evolutionary vector fields --which are the non-Abelian variational Lie algebroids' differentials-- with Lie algebra-valued zero-curvature representations for partial differential equations.

Let $A$ be a commutative, non-associative algebra over a field $\mathbb{F}$ of characteristic $\ne 2$. A half-axis in $A$ is an idempotent $e\in A$ such that $e$ satisfies the Peirce multiplication rules in a Jordan algebra, and, in…

We construct an L^2-model of "very small" irreducible unitary representations of simple Lie groups G which, up to finite covering, occur as conformal groups Co(V) of simple Jordan algebras V. If $V$ is split and G is not of type A_n, then…

A new algebra, hitherto not encountered in the usual Lie algebraic varieties or supervarieties, is introduced. The paper explores the rich and novel structure of the algebra, and it compares it on the one hand with the Jordan-Lie…

We study the structure of Lie groups admitting left invariant abelian complex structures in terms of commutative associative algebras. If, in addition, the Lie group is equipped with a left invariant Hermitian structure, it turns out that…

Jordan algebras arise naturally in (quantum) information geometry, and we want to understand their role and their structure within that framework. Inspired by Kirillov's discussion of the symplectic structure on coadjoint orbits, we provide…

We give the algebraic and geometric classification of complex four-dimensional Jordan superalgebras. In particular, we describe all irreducible components in the corresponding varieties.

Let $A$ be a unital algebra over a field $F$ with $\operatorname*{char} (F)\neq2$. In this paper we introduce a new concept of a generalized Jordan derivation, covering Jordan centralizers and Jordan derivations, as follows: a linear map…

We study so called regular Lie algebras, i.e. Lie algebras in which each nonzero element is regular. We make a connection with an open problem whether any element of reduced trace zero in a simple associative algebra is a commutator.

We classify, up to isomorphism, all gradings by an arbitrary abelian group on simple finitary Lie algebras of linear transformations (special linear, orthogonal and symplectic) on infinite-dimensional vector spaces over an algebraically…