Related papers: Lie higher derivations of arbitrary triangular alg…
It is well known that a finite-dimensional Lie algebra over a field of characteristic zero is simple exactly when its derivation algebra is simple. In this paper we characterize those Lie algebras of arbitrary dimension over any field that…
In this paper we shall consider the Lie algebra of column-finite infinite matrices indexed by positive integers $\mathbb{N}$, describe the lattice of its ideals for arbitrary field $K$ and study its derivations over any commutative, unital…
We determine the derivation algebras and the isomorphism classes of a family of the simple Lie algebras introduced recently by Xu [Manuscripta Math 100 (1999), 489-518]. The structure space of these algebras is given explicitly.
This is the first in a series of papers in which we study representations of the Brauer category and its allies. We define a general notion of triangular category that abstracts key properties of the triangular decomposition of a semisimple…
Recent theorems of Dubickas and Mossinghoff use auxiliary polynomials to give lower bounds on the Weil height of an algebraic number $\alpha$ under certain assumptions on $\alpha$. We prove a theorem which introduces an auxiliary polynomial…
We construct irreducible modules of centrally-extended classical Lie algebras over left ideals of the algebra of differential operators on the circle, through certain irreducible modules of centrally-extended classical Lie algebras of…
In this paper, we study triple derivations and triple homomorphisms of perfect Lie superalgebras over a commutative ring $R$. It is proved that, if the base ring contains $\frac{1}{2}$, $L$ is a perfect Lie superalgebra with zero center,…
A new C*-enlargement of a C*-algebra $A$ nested between the local multiplier algebra $M_{\text{loc}}(A)$ of $A$ and its injective envelope $I(A)$ is introduced. Various aspects of this maximal C*-algebra of quotients, $Q_{\text{max}}(A)$,…
Let M be a manifold and g a Lie algebra acting on M. Differential forms Omega(M) carry a natural action of Lie derivatives L(x) and contractions I(x) of fundamental vector fields for x \in g. Contractions (anti-) commute with each other,…
The additive (generalized) $\xi$-Lie derivations on prime algebras are characterized. It is shown, under some suitable assumption, that an additive map $L$ is an additive (generalized) Lie derivation if and only if it is the sum of an…
Triangular algebras, and maximal triangular algebras in particular, have been objects of interest for over fifty years. Rich families of examples have been studied in the context of many w$^*$- and C$^*$-algebras, but there remains a dearth…
In this work, we extend the definition of the graded prime ideals from those in commutative graded rings to the ideals over graded Lie algebras. We prove some facts about graded prime Lie ideals in arbitrary Lie algebras that are similar to…
The purpose of the present paper is to study representations and cohomologies of differential 3-Lie algebras with any weight. We introduce the representation of a differential 3-Lie algebra. Moreover,we develop cohomology theory of a…
We consider some special type extensions of an arbitrary Lie algebra, which we call universal extensions. We show that these extensions are in one-to-one correspondence with finite dimensional associative commutative algebras. We also…
We describe the branching of Lie algebras of classical type over $A_{n-1}$ using an inductive approach, which was motivated by the work of Gornitskii. This allows us to label the highest weight vectors of the modules occurring in the…
In this paper, first we introduce the notion of reflections on quadratic Rota-Baxter Lie algebras of weight $\lambda$, and show that they give rise to solutions of the classical reflection equation for the corresponding triangular Lie…
Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients are exhaustively described over both the complex and real fields. The exact lower and upper bounds for the dimensions of the maximal…
A bivariate representation of a complex simple Lie algebra is an irreducible representation having highest weight a combination of the first two fundamental weights. For a complex classical Lie algebra, we establish an expression for the…
We study an analogue of the Andreadakis-Johnson filtration for automorphism groups of free algebras and introduce the notion of tangent Lie algebras for certain automorphism groups, defined as subalgebras of the Lie algebra of derivations.…
Lie bialgebra contractions are introduced and classified. A non-degenerate coboundary bialgebra structure is implemented into all pseudo-orthogonal algebras $so(p,q)$ starting from the one corresponding to $so(N+1)$. It allows to introduce…