Let $ V $ be an $\mathbb {N} $-graded, simple, self-contragredient, $ C_2 $-cofinite vertex
operator algebra. We show that if the $ S $-transformation of the character of $ V $ is a linear …

We construct log-modular quantum groups at even order roots of unity, both as finite-
dimensional ribbon quasi-Hopf algebras and as finite ribbon tensor categories, via a de …

The main result is that the category of ordinary modules of an affine vertex operator algebra
of a simply laced Lie algebra at admissible level is rigid and thus a braided fusion category …

In this work, we introduce Urod algebras associated to simply laced Lie algebras as well as
the concept of translation of W-algebras. Both results are achieved by showing that the …

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 …

Here we define a series of associative algebras attached to a vertex operator algebra $ V $,
called mode transition algebras, showing they reflect both algebraic properties of $ V $ and …

We study relationships between the restricted unrolled quantum group U‾ q H (sl 2) at q= e π
i/r, and the singlet vertex operator algebra M (r), r≥ 2. We use deformable families of …

Abstract Suppose V^ G VG is the fixed-point vertex operator subalgebra of a compact group
G acting on a simple abelian intertwining algebra V. We show that if all irreducible V^ G VG …

Abstract Based on the Kazama–Suzuki type coset construction and its inverse coset
between the subregular W-algebras for sl n and the principal W-superalgebras for sl 1| n, we …

The interest in Logarithmic Conformal Field Theories (LCFTs) has been growing over the
last few years thanks to recent developments coming from various approaches. A …