The Hall algebra of a spherical object

TL;DR

This paper calculates the Hall algebra of a triangulated category generated by a spherical object, providing insights into its algebraic structure within the framework of Toen's definition.

Contribution

It explicitly determines the Hall algebra associated with a spherical object in a triangulated category, a novel computation in this context.

Findings

Explicit description of the Hall algebra for the spherical object category

Connections established with algebraic structures in triangulated categories

Provides a foundation for further algebraic and geometric investigations

Abstract

We determine the Hall algebra, in the sense of Toen, of the algebraic triangulated category generated by a spherical object.