相关论文: On the nature of the Virasoro algebra
Motivated by the work of Kupershmidt (J. Nonlin. Math. Phys. 6 (1998), 222 --245) we discuss the occurrence of left symmetry in a generalized Virasoro algebra. The multiplication rule is defined, which is necessary and sufficient for this…
For coprime $p,q\in\mathbb{Z}_{\geq 2}$, the triplet vertex operator algebra $W_{p,q}$ is a non-simple extension of the universal Virasoro vertex operator algebra of central charge $c_{p,q}=1-\frac{6(p-q)^2}{pq}$, and it is a basic example…
In this paper, we construct the super Virasoro algebra with an arbitrary conformal dimension $\Delta$ from the generalized $\mathcal{R}(p,q)$-deformed quantum algebra and investigate the $\mathcal{R}(p,q)$-deformed super Virasoro algebra…
It is shown that the elliptic algebra ${\cal A}_{q,p}(\hat{sl}(2)_c)$ at the critical level c=-2 has a multidimensional center containing some trace-like operators t(z). A family of Poisson structures indexed by a non-negative integer and…
In this paper, we study a certain deformation $D$ of the Virasoro algebra that was introduced and called $q$-Virasoro algebra by Nigro,in the context of vertex algebras. Among the main results, we prove that for any complex number $\ell$,…
We propose a q-difference version of the Drinfeld-Sokolov reduction scheme, which gives us q-deformations of the classical W-algebras by reduction from Poisson-Lie loop groups. We consider in detail the case of SL(2). The nontrivial…
A new 3-ary non-associative algebra, which is called a semi-associative $3$-algebra, is introduced, and the double modules and double extensions by cocycles are provided. Every semi-associative $3$-algebra $(A, \{ , , \})$ has an adjacent…
Given a locally finite graded set A and a commutative, associative operation on A that adds degrees, we construct a commutative multiplication * on the set of noncommutative polynomials in A which we call a quasi-shuffle product; it can be…
We construct operators t(z) in the elliptic algebra introduced by Foda et al. ${\cal A}_{q,p}({\hat sl}(2)_c)$. They close an exchange algebra when p^m=q^{c+2} for m integer. In addition they commute when p=q^{2k} for k integer non-zero,…
E.B. Vinberg's theory of quasi-derivations of algebras is extended to a broader framework of near-derivations. This deepens connections between Poisson geometry and Lie theory. Although basic results apply to arbitrary algebras, our…
We construct cocycles on the Lie algebra of pseudo- and q-pseudodifferential symbols of one variable and on their close relatives: the sine-algebra and the Poisson algebra on two-torus. A ``quantum'' Godbillon-Vey cocycle on…
Building on the work [18], where some standard basis for the queer $q$-Schur superalgebra $\mathcal{Q}_q(n,r;R)$ is defined by a labelling set of matrices and their associated double coset representatives, we investigate the matrix…
Virasoro-type symmetries and their roles in solvable models are reviewed. These symmetries are described by the two-parameter Virasoro-type algebra $Vir_{p,q}$ by choosing the parameters p and q suitably.
It is shown that a particular $q$-deformation of the Virasoro algebra can be interpreted in terms of the $q$-local field $\Phi (x)$ and the Schwinger-like point-splitted Virasoro currents, quadratic in $\Phi (x)$. The $q$-deformed Virasoro…
The fusion rules for the $(p,q)$-minimal model representations of the Virasoro algebra are shown to come from the group $G = \boZ_2^{p+q-5}$ in the following manner. There is a partition $G = P_1 \cup ...\cup P_N$ into disjoint subsets and…
Quasishuffle Hopf algebras, usually defined on a commutative monoid, can be more generally defined on any associative algebra V. If V is a commutative and cocommutative bialgebra, the associated quasishuffle bialgebra QSh(V) inherits a…
We find a nonsemisimple fusion algebra F_p associated with each (1,p) Virasoro model. We present a nonsemisimple generalization of the Verlinde formula which allows us to derive F_p from modular transformations of characters.
A construction of the Virasoro algebra in terms of free massless two-dimensional boson fields is studied. The ansatz for the Virasoro field contains the most general unitary scaling dimension 2 expression built from vertex operators. The…
We introduce an algebra of elliptic commuting variables involving a base $q$, nome $p$, and $2r$ noncommuting variables. This algebra, which for $r=1$ reduces to an algebra considered earlier by the author, is an elliptic extension of the…
In this paper, we construct a class of simple weight modules over the twisted Heisenberg-Virasoro algebra and gap-$p$ Virasoro algebras from restricted modules over some positive part subalgebra of the twisted Heisenberg-Virasoro algebra.…