Let V m,n p,q be the irreducible representation of the Virasoro algebra L with central charge cp,q = 1− 6(p − q) /pq and highest weight hm,n = [(np−mq)−(p−q)]/4pq, where p, q > 1 are relatively prime integers, and m, n are integers, such that 0 < m < p, 0 < n < q. For fixed p and q the representations V m,n p,q form the (p, q) minimal model of the Virasoro algebra [1]. For N > 0 let LN be the L...

There are also four appendices. Let K be a field of characteristic 0, and let C be a commutative K-algebra. which makes C into a Lie algebra, and is a biderivation (i.e. a derivation in each argument). The pair C, {−, −} is called a Poisson algebra. Poisson brackets arise in several ways. Example 1.1. Classical Hamiltonian mechanics. Here K = R, X is an even dimensional differentiable manifold ...

We study exceptional torsion in the integral cohomology of a family of p-groups associated to p-adic Lie algebras. A spectral sequence E r [g] is defined for any Lie algebra g which models the Bockstein spectral sequence of the corresponding group in characteristic p. This spectral sequence is then studied for complex semisimple Lie algebras like sln(C), and the results there are transferred to...

The PostLie algebra is an enriched structure of the Lie algebra that has recently arisen from operadic study. It is closely related to pre-Lie algebra, Rota-Baxter algebra, dendriform trialgebra, modified classical Yang-Baxter equations and integrable systems. This paper gives a complete classification of PostLie algebra structures on the Lie algebra sl(2,C) up to isomorphism. The classificatio...

Let $mathcal{A}$ be a $C^*$-algebra and $Z(mathcal{A})$ the‎ ‎center of $mathcal{A}$‎. ‎A sequence ${L_{n}}_{n=0}^{infty}$ of‎ ‎linear mappings on $mathcal{A}$ with $L_{0}=I$‎, ‎where $I$ is the‎ ‎identity mapping‎ ‎on $mathcal{A}$‎, ‎is called a Lie higher derivation if‎ ‎$L_{n}[x,y]=sum_{i+j=n} [L_{i}x,L_{j}y]$ for all $x,y in  ‎mathcal{A}$ and all $ngeqslant0$‎. ‎We show that‎ ‎${L_{n}}_{n...

We prove a fundamental case of a conjecture of the first author which expresses the homology of the extension of the Heisenberg Lie algebra by C[t]/(t) in terms of the homology of the Heisenberg Lie algebra itself. More specifically, we show that both the 0 and k + 1 x-graded components of homology of this extension of the 3-dimensional Heisenberg Lie algebra have dimension 3 by constructing a ...

This paper begins by introducing the concept of a quasi-hom-Lie algebra, or simply, a qhl-algebra, which is a natural generalization of hom-Lie algebras introduced in a previous paper [14]. Quasi-hom-Lie algebras include also as special cases (color) Lie algebras and superalgebras, and can be seen as deformations of these by homomorphisms, twisting the Jacobi identity and skew-symmetry. The nat...

We propose a Leibniz algebra, to be called DD$^+$, which is generalization of the Drinfel'd double. find that there one-to-one correspondence between DD$^+$ and Jacobi--Lie bialgebra, extending known Lie bialgebra then construct generalized frame fields $E_A{}^M\in\text{O}(D,D)\times\mathbb{R}^+$ satisfying algebra $\mathcal{L}_{E_A}E_B = - X_{AB}{}^C\,E_C\,$, where $X_{AB}{}^C$ are structure c...

let $mathcal m$ be a factor von neumann algebra. it is shown that every nonlinear $*$-lie higher derivation$d={phi_{n}}_{ninmathbb{n}}$ on $mathcal m$ is additive. in particular, if $mathcal m$ is infinite type $i$factor, a concrete characterization of $d$ is given.

A detailed description of the infinite-dimensional Lie algebra of ⋆-gauge transformations in noncommutative Yang-Mills theory is presented. Various descriptions of this algebra are given in terms of inner automorphisms of the underlying deformed algebra of functions on spacetime, of deformed symplectic diffeomorphisms, of the infinite unitary Lie algebra u(∞), and of the C∗-algebra of compact o...