Related papers: Vertex operator superalgebras and 16-fold way

We study operator algebras arising from monomial ideals in the ring of polynomials in noncommuting variables, through the apparatus of subproduct systems and C*-correspondences. We provide a full comparison amongst the related operator…

We describe the construction of the genus-zero parts of conformal field theories in the sense of G. Segal from representations of vertex operator algebras satisfying certain conditions. The construction is divided into four steps and each…

In this article, we describe the trace formulae of composition of several (up to four) adjoint actions of elements of the Lie algebra of a vertex operator algebra by using the Casimir elements. As an application, we give constraints on the…

Let V be a simple vertex operator algebra and G a finite automorphism group. Then there is a natural right G-action on the set of all inequivalent irreducible V-modules. Let S be a finite set of inequivalent irreducible V-modules which is…

We classify the irreducible modules for the fixed point vertex operator subebra of the rank 1 free bosonic VOA under the -1 automorphism.

In this paper, we introduce and study new classes of sub-vertex operator algebras of the lattice vertex operator algebras (VOAs), which we call the conic, Borel, and parabolic-type subVOAs. These CFT-type VOAs, which are not necessarily…

We study strongly graded vertex algebras and their strongly graded modules, which are conformal vertex algebras and their modules with a second, compatible grading by an abelian group satisfying certain grading restriction conditions. We…

A series of associative algebras $A_n(V)$ for a vertex operator algebra $V$ over an arbitrary algebraically closed field and nonnegative integers $n$ are constructed such that there is a one to one correspondence between irreducible…

We introduce a simple, self-dual, rational, and $C_2$-cofinite vertex operator algebra of CFT-type associated with a $\mathbb{Z}_k$-code for $k \ge 2$ based on the $\mathbb{Z}_k$-symmetry among the simple current modules for the parafermion…

The Heisenberg Oscillator Algebra admits irreducible representations both on the ring $B$ of polynomials in infinitely many indeterminates (the {\em bosonic representation}) and on a graded-by-{\em charge} vector space, the {\em…

Let V be a vertex operator algebra and g an automorphism of order T. We construct a sequence of associative algebras A_{g,n}(V) with n\in\frac{1}{T}\Z nonnegative such that A_{g,n}(V) is a quotient of A_{g,n+1/T}(V) and a pair of functors…

We consider the algebraic structure of $\mathbb{N}$-graded vertex operator algebras with conformal grading $V=\oplus_{n\geq 0} V_n$ and $\dim V_0\geq 1$. We prove several results along the lines that the vertex operators $Y(a, z)$ for $a$…

Let L_{B}(-5/2,0) (resp. L_{F}(-5/2,0)) be the simple vertex operator algebra associated to affine Lie algebra of type $B_{4}^{(1)}$ (resp. $F_{4}^{(1)}$) with the lowest admissible half-integer level -5/2. We show that L_{B}(-5/2,0) is a…

An explicit vertex operator algebra construction is given of a class of irreducible modules for toroidal Lie algebras.

Let $V_{L}$ be the vertex algebra associated to a non-degenerate even lattice $L$, $\theta$ the automorphism of $V_{L}$ induced from the $-1$ symmetry of $L$, and $V_{L}^{+}$ the fixed point subalgebra of $V_{L}$ under the action of…

Given a weight-one element $u$ of a vertex operator algebra $V$, we construct an automorphism of the category of generalized $g$-twisted modules for automorphisms $g$ of $V$ fixing $u$. We apply this construction to the case that $V$ is an…

A characterization of vertex operator algebra $V_L^+$ for any rank one positive definite even lattice $L$ is given in terms of dimensions of homogeneous subspaces of small weights. This result reduces the classification of rational vertex…

We state and prove a stratification result that allows us to classify the tensor ideal localizing subcategories for the stable module category $\text{Stab}(\mathcal{C}_{(\mathfrak{g}, \mathfrak{g}_{\bar 0})})$ of Lie superalgbera…

We construct integral forms containing the conformal vector $\omega$ in certain tensor powers of the Virasoro vertex operator algebra $L(\frac{1}{2},0)$, and we construct integral forms in certain modules for these algebras. When a triple…

The Monster Lie algebra $\mathfrak m$ is a quotient of the physical space of the vertex algebra $V=V^\natural\otimes V_{1,1}$, where $V^\natural$ is the Moonshine module vertex operator algebra of Frenkel, Lepowsky, and Meurman, and…