Related papers: Coset Vertex Operator Algebras and $\W$-Algebras

We study the Hecke algebra $\H(\bq)$ over an arbitrary field $\FF$ of a Coxeter system $(W,S)$ with independent parameters $\bq=(q_s\in\FF:s\in S)$ for all generators. This algebra is always linearly spanned by elements indexed by the…

Using two WZNW theories for Lie algebras $g$ and $h, h\subset g,$ we construct the associative quotient algebra which includes a class of $g/h$ coset primary fields and currents.

In this paper, first we introduce the notions of relative Rota-Baxter operators of nonzero weight on $3$-Lie algebras and $3$-post-Lie algebras. A 3-post-Lie algebra consists of a 3-Lie algebra structure and a ternary operation such that…

Let $\mathfrak{g}$ be a simple, finite-dimensional Lie (super)algebra equipped with an embedding of $\mathfrak{s} \mathfrak{l}_2$ inducing the minimal gradation on $\mathfrak{g}$. The corresponding minimal $\mathcal{W}$-algebra…

We give an algebraic proof of the unitarity of the vertex operator algebra $L(21/22, 0)\oplus L(21/22, 8)$ and of all its irreducible ordinary modules, using a coset realization arising from the $3C$-algebra. Motivated by the structure of…

A Lie algebra $L$ is said to be $(\Theta_{n},sl_{n})$-graded if it contains a simple subalgebra $\mathfrak{g}$ isomorphic to $sl_{n}$ such that the $\mathfrak{g}$-module $L$ decomposes into copies of the adjoint module, the trivial module,…

Noncommutative multivariable versions of weighted shifts arise naturally as `weighted' left creation operators acting on Fock space. We investigate the unital weak operator topology closed algebras they generate. The unweighted case yields…

Let $\mathfrak g$ be a symmetrizable Kac-Moody Lie algebra, and let $V_{\hat{\mathfrak g},\hbar}^\ell$, $L_{\hat{\mathfrak g},\hbar}^\ell$ be the quantum affine vertex algebras constructed in [11]. For any complex numbers $\ell$ and…

In this paper, irreducible modules of the diagonal coset vertex operator algebra $C(L_{\mathfrak{g}}(k+l,0),L_{\mathfrak{g}}(k,0)\otimes L_{\mathfrak{g}}(l,0))$ are classified under the assumption that…

We prove the longstanding physics conjecture that there exists a unique two-parameter $\mathcal{W}_{\infty}$-algebra which is freely generated of type $\mathcal{W}(2,3,\dots)$, and generated by the weights $2$ and $3$ fields. Subject to…

In this article, we describe the endomorphism ring of a finitely generated progenerator module of a weighted Leavitt path algebra $L_{K}(E, w)$ of a finite vertex weighted graph $(E, w)$. Contrary to the case of Leavitt path algebras, we…

The quantum weighted projective algebras $\mathbb{C}[\mathbb{WP}_{k,l,q}]$ are coinvariant subalgebras of the quantum group algebra $\mathbb{C}[SU_{q,2}]$. For each pair of indices $k,l$, two $2$-summable spectral triples will be…

In the first part of this paper, we discuss the classical W-algebra $\mathcal{W}(\mathfrak{g}, F)$ associated with a Lie superalgebra $\mathfrak{g}$ and the nilpotent element $F$ in an $\mathfrak{sl}_2$-triple. We find a generating set of…

Using the theory of vertex operator algebras and intertwining operators, we obtain presentations for the principal subspaces of all the standard $\widehat{\goth{sl}(3)}$-modules. Certain of these presentations had been conjectured and used…

One of the best understood families of logarithmic conformal field theories is that consisting of the (1,p) models (p = 2, 3, ...) of central charge c_{1,p} = 1 - 6 (p-1)^2 / p. This family includes the theories corresponding to the singlet…

In this work, we refine recent results on the explicit construction of polynomial algebras associated with commutants of subalgebras in enveloping algebras of Lie algebras by considering an additional grading with respect to the subalgebra.…

The extensions of the affine vertex operator algebras $L_{sl_2}(k,0)$ and the preunitary vertex operator algebras with central charges $c<1$ are classified. In particular, the unitary vertex operator algebras with central charges $c<1$ are…

Let $\mathfrak{g}$ be a basic Lie superalgebra and $f$ be an odd nilpotent element in an $\mathfrak{osp}(1|2)$ subalgebra of $\mathfrak{g}$. We provide a mathematical proof of the statement that the W-algebra $W^k(\mathfrak{g},F)$ for…

In this paper, we introduce the notion of modified Rota-Baxter operators of non-zero weight on $3$-Lie algebras and provide some examples. Next, we give various constructions of modified Rota-Baxter operators of non-zero weight according to…

Haisheng Li showed that given a module (W,Y_W(\cdot,x)) for a vertex algebra (V,Y(\cdot,x)), one can obtain a new V-module W^{\Delta} = (W,Y_W(\Delta(x)\cdot,x)) if \Delta(x) satisfies certain natural conditions. Li presented a collection…