Hall algebras via 2-Segal spaces
Abstract
This is an introduction to Hall algebras from the perspective of 2 2 -Segal spaces or, equivalently, decomposition spaces. We explain how linearizations of the 2 2 -Segal space arising as the Waldhausen S ∙ \mathcal {S}_{\bullet } -construction of a proto-exact category recover various previously known Hall algebras. We use the 2 2 -Segal perspective to study functoriality of the Hall algebra construction and explain how relative variants of 2 2 -Segal spaces lead naturally to representations of Hall algebras.
Fields of Study & Subjects
Algebraic structures and combinatorial models
Advanced Topics in Algebra
Advanced Operator Algebra Research
Publication details
- Journal / source
- Contemporary mathematics - American Mathematical Society
- Pages
- 97–130
- Publication date
- 1 January 2026
- Language
- EN