Related papers: The solenoidal Virasoro algebra and its simple wei…

We calculate explicitly the singular vectors of the Virasoro algebra with the central charge $c\leq 1$. As a result, we have an infinite sequence of the singular vectors for each Fock space with given central charge and highest weight, and…

Let $\mathcal{O}_c$ be the category of finite-length central-charge-$c$ modules for the Virasoro Lie algebra whose composition factors are irreducible quotients of reducible Verma modules. Recently, it has been shown that $\mathcal{O}_c$…

In this paper, we consider the modules for the Heisenberg-Virasoro algebra and the W algebra $W(2,2)$. We determine the modules whose restriction to the Cartan subalgebra (modulo center) are free of rank $1$ for the two algebras. We also…

Let $A_{m,n}$ be the tensor product of the Laurient polynomial algebra in $m$ even variables and the exterior algebra in $n$ odd variables over the complex field $\bC$, and the Witt superalgebra $W_{m,n}$ be the Lie superalgebra of…

In this paper, we study representations of non-finitely graded Lie algebras $\mathcal{W}(\epsilon)$ related to Virasoro algebra, where $\epsilon = \pm 1$. Precisely speaking, we completely classify the free $\mathcal{U}(\mathfrak…

For a simple, self-dual, strong CFT-type vertex operator algebra (VOA) of central charge $c$, we describe the Virasoro $n$-point correlation function on a genus $g$ marked Riemann surface in the Schottky uniformisation. We show that this…

In this paper, firstly we construct two classes of Lie conformal superalgebras denoted by $\mathcal{HVS}(\alpha)$ and $\mathcal{HVS}(\beta,\gamma,\tau)$, respectively, where $\alpha$ is an nonzero complex number and $\beta,\gamma,\tau$ are…

Let $\mathfrak g(G,\lambda)$ denote the deformed generalized Heisenberg-Virasoro algebra related to a complex parameter $\lambda\neq-1$ and an additive subgroup $G$ of $\mathbb C$. For a total order on $G$ that is compatible with addition,…

We study embeddings of the simple admissible affine vertex algebras $V_k(sl(2))$ and $V_k(osp(1,2))$, $k \notin {\Bbb Z}_{\ge 0}$, into the tensor product of rational Virasoro and $N=1$ Neveu-Schwarz vertex algebra with lattice vertex…

In this paper, we study the structure of Shen-Larsson modules over the Hamiltonian Lie algebra, also known as the Lie algebra of Hamiltonian vector fields on a torus. We establish necessary and sufficient conditions for the irreducibility…

We study permutation orbifolds of the $2$-fold and $3$-fold tensor product for the Virasoro vertex algebra $\mathcal{V}_c$ of central charge $c$. In particular, we show that for all but finitely many central charges…

Let $V_n=<e_1,...,e_{n+1}>$ be a vector products n-Lie algebra with n-Lie commutator $[e_1,...,\hat{e_i},...,e_{n+1}]=(-1)^ie_i$ over the field of complex numbers. Any finite-dimensional n-Lie $V_n$-module is completely reducible. Any…

In this paper we classify all irreducible cuspidal modules over a solenoidal Lie algebra over a rational quantum torus, generalizing the results in [BF2], [Su] and [Xu2].

In this paper, we generalize a result by Berman and Billig on weight modules over Lie algebras with polynomial multiplication. More precisely, we show that a highest weight module with an exp-polynomial ``highest weight'' has finite…

It has long been known that the moduli space of hyperbolic metrics on the disc can be identified with the Virasoro coadjoint orbit $\mathrm{Diff}^+(S^1) / \mathrm{SL}(2,\mathbb{R})$. The interest in this relationship has recently been…

We classify nontrivial deformations of the standard embedding of the Lie algebra $\Vect(S^1)$ of smooth vector fields on the circle, into the Lie algebra~$\PD(S^1)$ of pseudodifferential symbols on $S^1$. This approach leads to deformations…

J.~Lepowsky and R.~L.~Wilson initiated the approach to combinatorial Rogers-Ramanujan type identities via vertex operator constructions of standard (i.e. integrable highest weight) representations of affine Kac-Moody Lie algebras.…

In this paper, we consider the classification of irreducible ${\bf Z}$- and ${\bf Z}^2$-graded modules with finite dimensional homogeneous subspaces over the Virasoro-like algebra. We first prove that such a module is a uniformly bounded…

It is shown that the local quantum field theory of the chiral energy- momentum tensor with central charge $c=1$ coincides with the gauge invariant subtheory of the chiral $SU(2)$ current algebra at level 1, where the gauge group is the…

We consider a central extension of the sheaf of Lie algebras of maps from a manifold into a finite-dimensional simple Lie algebra, together with the sheaf of vector fields. Using vertex algebra methods we construct sheaves of modules for…