English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We study the braided monoidal structure that the fusion product induces onthe abelian category $\mathcal{W}_p$-mod, the category of representations ofthe triplet $W$-algebra $\mathcal{W}_p$. The $\mathcal{W}_p$-algebras are afamily of vertex operator algebras that form the simplest known examples ofsymmetry algebras of logarithmic conformal field theories. We formalise themethods for computing fusion products, developed by Nahm, Gaberdiel and Kausch,that are widely used in the physics literature and illustrate a systematicapproach to calculating fusion products in non-semi-simple representationcategories. We apply these methods to the braided monoidal structure of$\mathcal{W}_p$-mod, previously constructed by Huang, Lepowsky and Zhang, toprove that this braided monoidal structure is rigid. The rigidity of$\mathcal{W}_p$-mod allows us to prove explicit formulae for the fusion producton the set of all simple and all projective $\mathcal{W}_p$-modules, which werefirst conjectured by Fuchs, Hwang, Semikhatov and Tipunin; and Gaberdiel andRunkel.

The tensor structure on the representation category of the $\mathcal{W}_p$ triplet algebra