Vertex algebras are algebraic objects that encapsulate the concept of operator product
expansion from two-dimensional conformal field theory. Vertex algebras are fast becoming …

* Introduces the fundamental theory of vertex operator algebras and its basic techniques and
examples.* Begins with a detailed presentation of the theoretical foundations and proceeds …

Moonshine forms a way of explaining the mysterious connection between the monster finite
group and modular functions from classical number theory. The theory has evolved to …

We investigate trace functions of modules for vertex operator algebras (VOA) satisfying C 2-
cofiniteness. For the modular invariance property, Zhu assumed two conditions in Z:(1) A (V) …

Let V be a simple vertex operator algebra containing a rank n Heisenberg vertex algebra H
and let C= Com (H; V) be the coset of H in V. Assuming that the module categories of interest …

Let V be a simple vertex operator algebra and G a finite automorphism group of V such that
VG is regular. It is proved that every irreducible V G-module occurs in an irreducible g …

The congruence subgroup property is established for the modular representations
associated to any modular tensor category. This result is used to prove that the kernel of the …

These are lecture notes from author's mini-course on W-algebras during Session 1:“Vertex
algebras, W-algebras, and application” of INdAM Intensive research period “Perspectives in …

We relate commutative algebras in braided tensor categories to braid-reversed tensor
equivalences, motivated by vertex algebra representation theory. First, for C a braided …

Let V be a simple vertex operator algebra (VOA) and consider a representation category of V
that is a vertex tensor category in the sense of Huang–Lepowsky. In particular, this category …