Higher Categorical Aspects of Hall Algebras

  • Tobias Dyckerhoff
Chapter
Part of the Advanced Courses in Mathematics - CRM Barcelona book series (ACMBIRK)

Abstract

This chapter contains 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.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Tobias Dyckerhoff
    • 1
  1. 1.Hausdorff Center for Mathematics Villa MariaBonnGermany

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