A Rational Logarithmic Conformal Field Theory

TL;DR

This paper investigates the fusion properties of the triplet algebra at c=-2, revealing a finite set of representations, including irreducible and indecomposable reducible ones, that are closed under fusion.

Contribution

It demonstrates the existence of a finite, closed set of representations for the triplet algebra, including indecomposable reducible representations, expanding understanding of its structure.

Findings

Finite set of representations closed under fusion

Includes all irreducible and some reducible indecomposable representations

Provides insight into the algebra's fusion structure at c=-2

Abstract

We analyse the fusion of representations of the triplet algebra, the maximally extended symmetry algebra of the Virasoro algebra at c=-2. It is shown that there exists a finite number of representations which are closed under fusion. These include all irreducible representations, but also some reducible representations which appear as indecomposable components in fusion products.