Tropical friezes and the index in higher homological algebra

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Abstract

Cluster categories and cluster algebras encode two dimensional structures. For instance, the Auslander-Reiten quiver of a cluster category can be drawn on a surface, and there is a class of cluster algebras determined by surfaces with marked points. Cluster characters are maps from cluster categories (and more general triangulated categories) to cluster algebras. They have a tropical shadow in the form of so-called tropical friezes, which are maps from cluster categories (and more general triangulated categories) to the integers. This paper will define higher dimensional tropical friezes. One of the motivations is the higher dimensional cluster categories of Oppermann and Thomas, which encode (d + 1)-dimensional structures for an integer d â

OriginalsprogEngelsk
TidsskriftMathematical Proceedings of the Cambridge Philosophical Society
Vol/bind171
Nummer1
Sider (fra-til)23-49
Antal sider27
ISSN0305-0041
DOI
StatusUdgivet - jul. 2021
Udgivet eksterntJa

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