Related papers: Universal Central Extensions of the Matrix Leibniz…

In this work, we extend the central extension method for solvable Leibniz algebras. Using this method, a complete classification of one-dimensional abelian extensions of five-dimensional solvable Leibniz algebras with a non-trivial…

In this paper we describe solvable Leibniz algebras whose quotient algebra by one-dimensional ideal is a Lie algebra with rank equal to the length of the characteristic sequence of its nilpotent radical. We prove that such Leibniz algebra…

Given a von Neumann algebra $M$ we introduce so called central extension $mix(M)$ of $M$. We show that $mix(M)$ is a *-subalgebra in the algebra $LS(M)$ of all locally measurable operators with respect to $M,$ and this algebra coincides…

We study the Lie bialgebra structures that can be built on the one-dimensional central extension of the Poincar\'e and (A)dS algebras in (1+1) dimensions. These central extensions admit more than one interpretation, but the simplest one is…

The extension structure of the 2-dimensional current algebra of non-linear sigma models is analysed by introducing Kostant Sternberg $(L,M)$ systems. It is found that the algebra obeys a two step extension by abelian ideals. The second step…

In this paper we identify the structure of complex finite-dimensional Leibniz algebras with associated Lie algebras $sl_2^1\oplus sl_2^2\oplus \dots \oplus sl_2^s\oplus R,$ where $R$ is a solvable radical. The classifications of such…

Finite dimensional modular Lie superalgebras over algebraically closed fields with indecomposable Cartan matrices are classified under some technical, most probably inessential, hypotheses. If the Cartan matrix is invertible, the…

In this paper we prove that the subalgebras of cocommutative elements in the quantized coordinate rings of $M_{n}$, $GL_{n}$ and $SL_{n}$ are the centralizers of the trace $x_{1,1}+\dots+x_{n,n}$ in each algebra, for…

For any finite dimensional Lie superalgebra $\dot{\mathfrak{g}}$ (maybe a Lie algebra) with an even derivation $d$ and a finite order automorphism $\sigma$ that commutes with $d$, we introduce the $(d,\sigma)$-twisted Affine-Virasoro…

Let $n\geq 2$ be an integer, $p$ be a prime number and $K$ be a finite extension of $\mathbb{Q}_p$. Motivated by Schraen's thesis and Gehrmann's definition of automorphic simple $\mathscr{L}$-invariants, we study the first non-vanishing…

The associative ring $R(P(t))=\mathbb C[t^{\pm1},u \,|\, u^2=P(t)]$, where $P(t)=\sum_{i=0}^na_it^i=\prod_{k=1}^n(t-\alpha_i)$ with $\alpha_i\in\mathbb C$ pairwise distinct, is the coordinate ring of a hyperelliptic curve. The Lie algebra…

We obtain an embedding of a one-parameter family of exceptional simple Lie superalgebras $D(2, 1 ; \alpha)$ into the Lie superalgebra of pseudodifferential symbols on the supercircle $S^{1|2}$. Correspondingly, there is an embedding of…

We classify anti-involutions of Lie superalgebra $\hsd$ preserving the principal gradation, where $\hsd$ is the central extension of the Lie superalgebra of differential operators on the super circle $S^{1|1}$. We clarify the relations…

We study the non-trivial central extensions $CEHeis$ of the Heisenberg algebra $Heis$ recently constructed in {AccBouCE}. We prove that a real form of $CEHeis$ is one the fifteen classified real four--dimensional solvable Lie algebras. We…

The aim of this paper is to study the $(\alpha, \gamma)$-prolongation of central extensions. We obtain the obstruction theory for $(\alpha, \gamma)$-prolongations and classify $(\alpha, \gamma)$-prolongations thanks to low-dimensional…

The central extension of the mapping class groups of punctured surfaces of finite type that arises in quantum Teichm\"uller theory is 12 times the Meyer class plus the Euler classes of the punctures. This is analogous to the result obtained…

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…

From the four normed division algebras--the real numbers, complex numbers, quaternions and octonions, of dimension k=1, 2, 4 and 8, respectively--a systematic procedure gives a 3-cocycle on the Poincare superalgebra in dimensions k+2=3, 4,…

We consider the maximal central extension of the supertranslation algebra in d=4 and 3, which includes tensor central charges associated to topological defects such as domain walls (membranes) and strings. We show that for all N-extended…

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…