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

The quantum loop algebra $U_{v}(\mathcal{L}\mathfrak{g})$ was defined as ageneralization of the Drinfeld's new realization of the quantum affine algebrato the loop algebra of any Kac-Moody algebra $\mathfrak{g}$. It has been shownby Schiffmann that the Hall algebra of the category of coherent sheaves on aweighted projective line is closely related to the quantum loop algebra$U_{v}(\mathcal{L}\mathfrak{g})$, for some $\mathfrak{g}$ with a star-shapedDynkin diagram. In this paper we study Drinfeld's presentation of$U_{v}(\mathcal{L}\mathfrak{g})$ in the double Hall algebra setting, based onSchiffmann's work. We explicitly find out a collection of generators of thedouble composition algebra $\mathbf{DC}(\Coh(\mathbb{X}))$ and verify that theysatisfy all the Drinfeld relations.

Hall algebra approach to Drinfeld's presentation of quantum loop algebras