We prove the conjecture of Gaiotto and Rap\v {c}\'ak that the $ Y $-algebras $ Y_ {L, M,
N}[\psi] $ with one of the parameters $ L, M, N $ zero, are simple one-parameter quotients of …

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

Given a finite-dimensional reductive Lie algebra g equipped with a nondegenerate,
invariant, symmetric bilinear form B, let V k (g, B) denote the universal affine vertex algebra …

Let gg be a simple, finite-dimensional Lie (super) algebra equipped with an embedding of sl
_2 sl 2 inducing the minimal gradation on g g. The corresponding minimal W W-algebra W …

We present a systematic study of the orbifolds of the rank $ n $ symplectic fermion algebra
$\mathcal {A}(n) $, which has full automorphism group $ Sp (2n) $. First, we show that …

The Lie superalgebra $\mathcal {S}\mathcal {D} $ of regular differential operators on the
super circle has a universal central extension $\widehat {\mathcal {S}\mathcal {D}} $. For …

Coset constructions of-algebras have many applications and were recently given for
principal-algebras of,, and types by Arakawa together with the 1st and 3rd authors. In this …

Let $\mathcal {W}^ k (\mathfrak {sl} _4, f_ {\text {subreg}}) $ be the universal $\mathcal {W} $-
algebra associated to $\mathfrak {sl} _4 $ with its subregular nilpotent element, and let …

The invariant subalgebra \mathcalH^+ of the Heisenberg vertex algebra \mathcalH under its
automorphism group \mathbbZ/2\mathbbZ was shown by Dong–Nagatomo to be a …