Related papers: Reduction Groups and Automorphic Lie Algebras

We show how various constructions of $\mathbb{Z}$-graded Lie superalgebras are related to each other. These Lie superalgebras have a Lie algebra $\mathfrak{g}$ as the subalgebra at degree 0, an odd $\mathfrak{g}$-module V as the subspace at…

In this paper, we discuss the inducibility problem for automorphisms of multiplicative Lie algebra extensions and show that obstruction to the inducibility of pairs lies in the second cohomology group of multiplicative Lie algebras. We also…

The affine group scheme of automorphisms of an evolution algebra that is equal to its square, is shown to lie in an exact sequence, such that the other terms depend solely on the directed graph associated to the algebra. As a consequence,…

This work pioneers the systematic study and classification (up to Lie algebra automorphisms) of finite-dimensional coboundary Lie bialgebras through Grassmann algebras. Several mathematical structures on Lie algebras, e.g. Killing forms or…

We classify up to isomorphism the gradings by arbitrary groups on the exceptional classical simple Lie superalgebras $G(3)$, $F(4)$ and $D(2,1;\alpha)$ over an algebraically closed field of characteristic $0$. To achieve this, we apply the…

A study is made of real Lie algebras admitting a hypersymplectic structure, and we provide a method to construct such hypersymplectic Lie algebras. We use this method in order to obtain the classification of all hypersymplectic structures…

This paper deals with affine connections on real manifolds. We give a new characterization of flat affine connections on real manifolds by means of certain affine representations of the Lie group of automorphisms preserving the connection.…

We first recall two equivalent definitions of Lie $2$-algebras, categorification of Lie algebras and $2$-term $L_\infty$-algebras. Then we present four different kinds of Lie $2$-algebras from $2$-plectic manifolds, Courant algebroids,…

The main purpose of this work is to develop the basic notions of the Lie theory for commutative algebras. We introduce a class of $\mathbbZ_2$-graded commutative but not associative algebras that we call ``Lie antialgebras''. These algebras…

In this paper, we study the derivations, central extensions and the automorphisms of the infinite-dimensional Lie algebra W which appeared in [8] and Dong-Zhang's recent work [22] on the classification of some simple vertex operator…

This paper concerns the problem of classifying finite-dimensional real solvable Lie algebras whose derived algebras are of codimension 1 or 2. On the one hand, we present an effective method to classify all $(n+1)$-dimensional real solvable…

This is a short survey on the recent developments made in the integration theory with effective formulas of algebraic structures stronger or higher than Lie algebras.

We study finite-dimensional nonassociative algebras. We prove the implicit function theorem for such algebras. This allows us to establish a correspondence between such algebras and quasigroups, in the spirit of classical correspondence…

In this paper, we introduce two new families of infinite-dimensional simple Lie algebras and a new family of infinite-dimensional simple Lie superalgebras. These algebras can be viewed as generalizations of the Block algebras.

We associate elliptic affine Lie algebras with what are called vertex $\C((z))$-algebras and their modules in a certain category. In the course, we construct two families of Lie algebras closely related to elliptic affine Lie algebras.

In this paper a finite dimensional unital associative algebra is presented, and its group of algebra automorphisms is detailed. The studied algebra can physically be understood as the creation operator algebra in a formal quantum field…

We give a full classification of 6-dimensional nilpotent Lie algebras over an arbitrary field, including fields that are not algebraically closed and fields of characteristic~2. To achieve the classification we use the action of the…

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…

We present an overview of characteristic identities for Lie algebras and superalgebras. We outline methods that employ these characteristic identities to deduce matrix elements of finite dimensional representations. To demonstrate the…

We study the automorphism groups of finite-dimensional cyclic Leibniz algebras. In this connection, we consider the relationships between groups, modules over associative rings and Leibniz algebras.