相关论文: On simple real Lie bialgebras

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…

The affine space of traceless complex matrices in which the sum of all elements in every row and every column is equal to one is presented as an example of an affine space with a Lie bracket or a Lie affgebra.

Motivated by the recent progress towards classification of simple finite-dimensional Lie algebras over an algebraically closed field of characteristic $2$, we investigate such $15$-dimensional algebras.

In this paper, under some natural condition, a complete classification of compatible left-symmetric conformal algebraic structures on the Lie conformal algebra $\mathcal{W}(a,b)$ is presented. Moreover, applying this result, we obtain a…

The main definitions and properties of Lie superalgebras are proposed a la facon de a short dictionary, the different items following the alphabetical order. The main topics deal with the structure of simple Lie superalgebras and their…

We introduce 3-irreducible modules, even roots and odd roots for Leibniz algebras, produce a basis for a root space of a Leibniz algebra with a semisimple Lie factor, and classify finite dimensional simple Leibniz algebras with Lie factor…

Lie brackets or Lie affgebra structures on several classes of affine spaces of matrices are studied. These include general normalised affine matrices, special normalised affine matrices, anti-symmetric and anti-hermitian normalised affine…

We determine all spherical algebraic subalgebras in any simple Lie algebra of real rank 1.

We provide explicit formulas for the number of ad-nilpotent ideals of a Borel subalgebra of a complex simple Lie algebra having fixed class of nilpotence.

In this paper, Lie bialgebra structures on the extended Schrodinger-Virasoro Lie algebra are classified. It is obtained that all the Lie bialgebra structures on L are triangular coboundary. As a by-product, it is derived that the first…

In this paper, we classify the following simple $\mathbb{Z}$-graded Lie conformal algebras $\mathcal{L}=\bigoplus_{i\in \mathbb{Z}}\mathcal{L}_i$ such that (1)$rank\mathcal{L}_i\leq 1$, (2)$\mathcal{L}_0$ is the Virasoro Lie conformal…

The paper concerns two versions of the notion of real forms of Lie superalgebras. One is the standard approach, where a real form of a complex Lie superalgebra is a real Lie superalgebra such that its complexification is the original…

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…

Every metric symplectic Lie algebra has the structure of a quadratic extension. We give a standard model and describe the equivalence classes on the level of corresponding quadratic cohomology sets. Finally, we give a scheme to classify the…

We show that any proper Lie groupoid admits a compatible (real) analytic structure.

Let $k$ be a field of characteristic not two or three. We classify up to isomorphism all finite-dimensional Lie superalgebras $\mathfrak{g}=\mathfrak{g}_0\oplus \mathfrak{g}_1$ over $k$, where $\mathfrak{g}_0$ is a three-dimensional simple…

It is known that the category of Lie algebras over a ring admits algebraic exponents. The aim of this paper is to show that the same is true for the category of internal Lie algebras in an additive, cocomplete, symmetric, closed, monoidal…

In this paper we prove that every recursively presented Lie algebra over a field which is a finite extention of its simple subfield can be embedded in a recursively presented Lie algebra defined by relations which are equalities of…

A new structure, based on joining copies of a group by means of a \emph{twist}, has recently been considered to describe the brackets of the two exceptional real Lie algebras of type $G_2$ in a highly symmetric way. In this work we show…

This paper presents a survey of the results and ideas behind the classification of the fine gradings, up to equivalence, on the simple finite dimensional Lie algebras over an algebraically closed field of characteristic zero. It provides an…