The Triplet Vertex Operator Algebra W(p) and the Restricted Quantum Group at Root of Unity

TL;DR

This paper establishes an equivalence between the module categories of the triplet vertex operator algebra W(p) and the quantum algebra of type sl_2 at a root of unity, linking two important algebraic structures.

Contribution

It proves the abelian category of W(p) modules is equivalent to that of the restricted quantum group at a root of unity, revealing a deep connection between VOA and quantum group representations.

Findings

Category equivalence between W(p) modules and quantum sl_2 modules

Bridges VOA theory with quantum group at roots of unity

Provides new tools for studying logarithmic CFTs and quantum algebra

Abstract

We prove the abelian category of the modules over triplet VOA W(p) is category equivalent to the abelian category of the modules over quantum algebra of type sl_2 at root of unity.