Hall algebras via 2-Segal spaces

Benjamin Cooper; Matthew B Young

doi:10.48550/arxiv.2409.19384

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Hall algebras via 2-Segal spaces

Benjamin Cooper and Matthew B Young

ArXiv.org

Cornell University

09/28/2024

DOI: 10.48550/arxiv.2409.19384

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Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

This is an introduction to Hall algebras from the perspective of 2-Segal spaces or decomposition spaces, as introduced by Dyckerhoff and Kapranov and Gálvez-Carrillo, Kock and Tonks, respectively. We explain how linearizations of the 2-Segal space arising as the Waldhausen S∙-construction of a proto-exact category recover various previously known Hall algebras. We use the 2-Segal perspective to study functoriality of the Hall algebra construction and explain how relative variants of 2-Segal spaces lead naturally to representations of Hall algebras.

Mathematics - Algebraic Topology

Mathematics - Category Theory

Mathematics - Representation Theory

Details

Title: Subtitle: Hall algebras via 2-Segal spaces
Creators: Benjamin Cooper
Matthew B Young
Resource Type: Preprint
Publication Details: ArXiv.org
DOI: 10.48550/arxiv.2409.19384
ISSN: 2331-8422
Publisher: Cornell University; Ithaca, New York
Language: English
Date posted: 09/28/2024
Academic Unit: Mathematics
Record Identifier: 9984721138502771

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