Higher categorical aspects of Hall Algebras

Abstract

These are extended notes for a series of lectures on Hall algebras given at the CRM Barcelona in February 2015. The basic idea of the theory of Hall algebras is that the collection of flags in an exact category encodes an associative multiplication law. While introduced by Steinitz and Hall for the category of abelian p-groups, it has since become clear that the original construction can be applied in much greater generality and admits numerous useful variations. These notes focus on higher categorical aspects based on the relation between Hall algebras and Waldhausen's S-construction.

60 pages, preliminary version, comments very welcome

References in corpus (4)

• Triangulated surfaces in triangulated categories
• Lectures on Hall algebras
• A Categorification of Hall Algebras
• Decomposition Spaces, Incidence Algebras and Möbius Inversion

Cited by in corpus (8)

• Decomposition spaces, incidence algebras and Möbius inversion I: basic theory
• Higher Segal structures in algebraic $K$-theory
• Decomposition spaces and restriction species
• 2-Segal spaces as invertible infinity-operads
• The incidence comodule bialgebra of the Baez-Dolan construction
• A geometric approach to Hall algebras I: Higher Associativity
• The universal Hall bialgebra of a double 2-Segal space
• Equivariant motivic Hall algebras