A Serre Relation in the $K$-theoretic Hall algebra of surfaces

TL;DR

This paper proves a Serre relation within the $K$-theoretic Hall algebra of surfaces, advancing the understanding of algebraic structures related to surfaces in algebraic geometry.

Contribution

It establishes a Serre relation in the $K$-theoretic Hall algebra of surfaces, a key step in understanding its algebraic structure.

Findings

Proved a Serre relation in the $K$-theoretic Hall algebra of surfaces.

Connected the algebraic structure to geometric constructions by Kapranov-Vasserot.

Enhanced the theoretical framework of Hall algebras in algebraic geometry.

Abstract

We prove a Serre relation in the $K$-theoretic Hall algebra of surfaces constructed by Kapranov-Vasserot and the second author.