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 consider the motivic Hall algebra of coherent sheaves over an irreduciblereduced projective curve of arithmetic genus $1$. We introduce the compositionsubalgebra in the singular curve case, and show that it is isomorphic to thecomposition subalgebra for a smooth elliptic curve. As in the case of smoothelliptic case studied by Burban and Schiffmann, the reduced Drinfeld double ofthe composition subalgebra is isomorphic to the quantum toroidal algebra for$\mathfrak{gl}_1$ (also called Ding-Iohara-Miki algebra), and it inheritsautomorphisms induced from equivalences of the associated derived category. Weshow that one of the non-trivial automorphisms coincide with the oneconstructed by Miki in a purely algebraic manner.

Quantum toroidal algebras and motivic Hall algebras I. Hall algebras for singular elliptic curves