TY - JOUR
T1 - Tropical friezes and the index in higher homological algebra
AU - Jorgensen, Peter
N1 - Publisher Copyright:
© 1. They are (d + 2)-Angulated categories, which belong to the subject of higher homological algebra. We will define higher dimensional tropical friezes as maps from higher cluster categories (and more general (d + 2)-Angulated categories) to the integers. Following Palu, we will define a notion of (d + 2)-Angulated index, establish some of its properties, and use it to construct higher dimensional tropical friezes.
PY - 2021/7
Y1 - 2021/7
N2 - 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
AB - 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
KW - 2010 Mathematics Subject Classification: 05E15 16G10 18E10 18E30
UR - http://www.scopus.com/inward/record.url?scp=85082507810&partnerID=8YFLogxK
U2 - 10.1017/S0305004120000031
DO - 10.1017/S0305004120000031
M3 - Journal article
AN - SCOPUS:85082507810
SN - 0305-0041
VL - 171
SP - 23
EP - 49
JO - Mathematical Proceedings of the Cambridge Philosophical Society
JF - Mathematical Proceedings of the Cambridge Philosophical Society
IS - 1
ER -