Related papers: Central extensions of the Heisenberg algebra

The coefficient algebra of a finite-dimensional Lie algebra on a finite-dimensional representation is defined as the subalgebra generated by all coefficients of the corresponding characteristic polynomial. We explore connections between…

Let $A \subseteq E$ be a given extension of Hopf (respectively Lie) algebras. We answer the \emph{classifying complements problem} (CCP) which consists of describing and classifying all complements of $A$ in $E$. If $H$ is a given…

Let $M$ be a manifold with a closed, integral $(k+1)$-form $\omega$, and let $G$ be a Fr\'echet-Lie group acting on $(M,\omega)$. As a generalization of the Kostant-Souriau extension for symplectic manifolds, we consider a canonical class…

For a Hecke pair $(G, H)$ and a finite-dimensional representation $\sigma$ of $H$ on $V_\sigma$ with finite range we consider a generalised Hecke algebra $\H_\sigma(G, H)$, which we study by embedding the given Hecke pair in a Schlichting…

We introduce a commutative associative graded algebra structure on the direct sum Z of the centers of the Hecke algebras associated to the symmetric groups in n letters for all n. As a natural deformation of the classical construction of…

In this paper, we classify solvable Lie algebras of dimensions $\leq 8$ endowed with a nondegenerate invariant symmetric bilinear form over an algebraically closed field. This classification (up to isometrically isomorphisms) is mainly…

We investigate the structure and representation theory of finite-dimensional $\mathbb{Z}$-graded Lie algebras, including the corresponding root systems and Verma, irreducible, and Harish-Chandra modules. This extends the familiar theory for…

In this paper we introduce the notion of pure non-characteristically nilpotent Lie algebra and under a condition we prove that a complex maximal extension of a finite-dimensional pure non-characteristically nilpotent Lie algebra is…

In this paper, we study the theory of non-abelian extensions of a Leibniz conformal algebra $R$ by a Leibniz conformal algebra $H$ and prove that all the non-abelian extensions are classified by non-abelian $2$nd cohomology $H^2_{nab}(R,H)$…

The aim of this paper is to introduce and study quadratic Hom-Lie algebras, which are Hom-Lie algebras with symmetric invariant nondegenerate bilinear forms. We provide several constructions leading to examples and extend the double…

Lax operator algebras were introduced by Krichever and Sheinman as a further development of I.Krichever's theory of Lax operators on algebraic curves. These are almost-graded Lie algebras of current type. In this article local cocycles and…

As well known that it is no way to do the abstract harmonic analysis on the non connected Lie groups. The goal of this paper is to draw the attention of Mathematicians to solve this problem. therefore let R be the group of nonzero real…

We study the centralizer of a parabolic subalgebra in the Hecke algebra associated with an arbitrary (possibly infinite) Coxeter group. While the center and cocenter have been extensively studied in the finite and affine cases, much less is…

In this paper we study a special subclass of real solvable Lie algebras having small dimensional or small codimensional derived ideal. It is well-known that the derived ideal of any Heisenberg Lie algebra is 1-dimensional and the derived…

This paper mainly studies the ResLieDer pair in characteristic 2, that is, a restricted Lie algebra with a restricted derivation. We define the restricted representation of a ResLieDer pair and the corresponding cohomology complex. We show…

Graded Hecke algebras can be constructed in terms of equivariant cohomology and constructible sheaves on nilpotent cones. In earlier work, their standard modules and their irreducible modules where realized with such geometric methods. We…

In this paper, we introduced the notion of Hom-Lie antialgebras. The representations and cohomology theory of Hom-Lie antialgebras are investigated. We prove that the equivalent classes of abelian extensions of Hom-Lie antialgebras are in…

We provide a rigorous mathematical foundation to the study of strongly rational, holomorphic vertex operator algebras V of central charge c = 8, 16 and 24 initiated by Schellekens. If c = 8 or 16 we show that V is isomorphic to a lattice…

Following arXiv:0909.5586 and arXiv:1411.4125, we construct two super-extensions of the usual tensor algebra through the super-actions of symmetric groups and Hecke algebras respectively. For each extension, we consider a special type of…

We generalize to the case of Lie superalgebras the classical symplectic double extension of symplectic Lie algebras introduced in [2]. We use this concept to give an inductive description of nilpotent homogeneous-symplectic Lie…