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

Let $U_\varepsilon^{\mathrm{res}}(L\mathfrak{sl}_2)$ be the restrictedintegral form of the quantum loop algebra $U_q(L\mathfrak{sl}_2)$ specialisedat a root of unity $\varepsilon$. We prove that the Grothendieck ring of atensor subcategory of representations of$U_\varepsilon^{\mathrm{res}}(L\mathfrak{sl}_2)$ is a generalised clusteralgebra of type $C_{l-1}$, where $l$ is the order of $\varepsilon^2$. Moreover,we show that the classes of simple objects in the Grothendieck ring essentiallycoincide with the cluster monomials. We also state a conjecture for$U_\varepsilon^{\mathrm{res}}(L\mathfrak{sl}_3)$, and we prove it for $l=2$.

Quantum affine algebras at roots of unity and generalised cluster algebras