Related papers: Some isomorphisms between exceptional W-algebras
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 study automorphic Lie algebras and their applications to integrable systems. Automorphic Lie algebras are a natural generalisation of celebrated Kac-Moody algebras to the case when the group of automorphisms is not cyclic. They are…
With the introduction of special roots, we show the existence of some special weights with quite interesting properties for finite Lie algebras. We propose and discuss two statements which lead us to an explicit construction of these…
We give explicit formulas proving restrictedness of the following Lie (super)algebras: known exceptional simple vectorial Lie (super)algebras in characteristic 3, deformed Lie (super)algebras with indecomposable Cartan matrix, and (under…
We consider a method popular in the literature of associating a two-step nilpotent Lie algebra with a finite simple graph. We prove that the two-step nilpotent Lie algebras associated with two graphs are Lie isomorphic if and only if the…
We consider the natural Lie algebra structure on the (associative) group algebra of a finite group $G$, and show that the Lie subalgebras associated to natural involutive antiautomorphisms of this group algebra are reductive ones. We give a…
In recent years, the notion of characteristic polynomial of representations of Lie algebras has been widely studied. This paper provides more properties of these characteristic polynomials. For simple Lie algebras, we characterize the…
We characterize finite-dimensional Lie algebras over an arbitrary field of characteristic zero which admit a non-trivial (quasi-) triangular Lie bialgebra structure.
A pseudo $H$-type Lie algebra naturally gives rise to a conformal pseudo-subriemannian fundamental graded Lie algebras. In this paper we investigate the prolongations of the associated fundamental graded Lie algebra and the associated…
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…
In a paper by Michaelis a class of infinite-dimensional Lie bialgebras containing the Virasoro algebra was presented. This type of Lie bialgebras was classified by Ng and Taft. In this paper, all Lie bialgebra structures on the Lie algebras…
A catalogue of explicit realizations of representations of (super) Lie algebras and quantum algebras in Fock space is presented.
In this paper, the author gives two methods to construct complete Lie algebras. Both methods show that the derivation algebras of some Lie algebras are complete.
A simple unifying view of the exceptional Lie algebras is presented. The underlying Jordan pair content and role are exhibited. Each algebra contains three Jordan pairs sharing the same Lie algebra of automorphisms and the same external…
In this paper we prove several theorems about the behavior of index of Lie algebras derived from associative algebras under tensor products of underlying associative algebras.
We give a complete description of ring isomorphisms between algebras of measurable operators affiliated with von Neumann algebras of type II$_1.$
Sometimes, mathematical oddities crowd in upon one another, and the exceptions to one classification scheme reveal themselves as fellow-travelers with the exceptions to a quite different taxonomy.
In this paper we construct compact forms associated with a complex Lie supergroup with Lie superalgebra of classical type.
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.
We derive explicit formulas for the inverses of the Cartan matrices of the simple Lie algebras and the basic classical Lie superalgebras, as well as for their infinite generalizations.