Related papers: The Universal Central Extension of the Three-point…
The recent investigation of the gauge structure of extended geometry is generalised to situations when ancillary transformations appear in the commutator of two generalised diffeomorphisms. The relevant underlying algebraic structure turns…
This paper presents new generators for the center of the universal enveloping algebra of the symplectic Lie algebra. These generators are expressed in terms of the column-permanent, and it is easy to calculate their eigenvalues on…
We construct a central extension of the smooth Deligne cohomology group of a compact oriented odd dimensional smooth manifold, generalizing that of the loop group of the circle. While the central extension turns out to be trivial for a…
We investigate possibility of central extension for non-relativistic conformal algebras in 1+1 dimension. Three different forms of charges can be suggested. A trivial charge for temporal part of the algebra exists for all elements of…
We construct homology with trivial coefficients of Hom-Leibniz $n$-algebras. We introduce and characterize universal ($\alpha$)-central extensions of Hom-Leibniz $n$-algebras. In particular, we show their interplay with the zeroth and first…
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 this paper, Lie superbialgebra structures on the centerless twisted N=2 superconformal algebra $\LL$ are considered which are proved to be coboundary triangular.
S-expansions of three-dimensional real Lie algebras are considered. It is shown that the expansion operation allows one to obtain a non-unimodular Lie algebra from a unimodular one. Nevertheless S-expansions define no ordering on the…
In this paper, we introduce the notion of generalized representation of a $3$-Lie algebra, by which we obtain a generalized semidirect product $3$-Lie algebra. Moreover, we develop the corresponding cohomology theory. Various examples of…
The paper concerns perfect diassociative algebras and their implications to the theory of central extensions. It is first established that perfect diassociative algebras have strong ties with universal central extensions. Then, using a…
In 1992 A. Zhedanov introduced the Askey-Wilson algebra AW=AW(3) and used it to describe the Askey-Wilson polynomials. In this paper we introduce a central extension $\Delta$ of AW, obtained from AW by reinterpreting certain parameters as…
In the context of internal crossed modules over a fixed base object in a given semi-abelian category, we use the non-abelian tensor product in order to prove that an object is perfect (in an appropriate sense) if and only if it admits a…
In this work, we consider Lie algebras L containing a subalgebra isomorphic to sl3 and such that L decomposes as a module for that sl3 subalgebra into copies of the adjoint module, the natural 3-dimensional module and its dual, and the…
We obtain a recurrent and monotone method for constructing and classifying nilpotent Lie algebras by means of successive central extensions. It consists in calculating the second cohomology of an extendable nilpotent Lie algebra with the…
We study the graded Lie algebra $L(RC_K)$ associated with the lower central series of a right-angled Coxeter group. We construct a surjective homomorphism from the polynomial ring over an explicit Lie algebra $N_K$ to the commutator…
We prove that linear groups over rings of non-commutative Laurent polynomials $D_{\tau}$ have Tits systems with the corresponding affine Weyl groups and have universal central extensions if $|Z(D)|\geq 5$ and $|Z(D)|\neq 9$. We also…
Motivated by positive energy representations, we classify those continuous central extensions of the compactly supported gauge Lie algebra that are covariant under a 1-parameter group of transformations of the base manifold.
We study the skew-symmetric prolongation of a Lie subalgebra $\g \subseteq \mathfrak{so}(n)$, in other words the intersection $\Lambda^3 \cap (\Lambda^1 \otimes \g)$.We compute this space in full generality. Applications include uniqueness…
The purpose of this paper is twofold. First, we introduce the notions of left-symmetric and left alternative structures on superspaces in characteristic 2. We describe their main properties and classify them in dimension 2. We show that…
The $q$-Onsager algebra $O_q$ is presented by two generators $W_0$, $W_1$ and two relations, called the $q$-Dolan/Grady relations. Recently Baseilhac and Koizumi introduced a current algebra $\mathcal A_q$ for $O_q$. Soon afterwards,…