Super Caldero--Chapoton map for type $A$
Representation Theory
2024-03-05 v2 Combinatorics
Rings and Algebras
Abstract
One can explicitly compute the generators of a surface cluster algebra either combinatorially, through dimer covers of snake graphs, or homologically, through the CC-map applied to indecomposable modules over the appropriate algebra. Recent work by Musiker, Ovenhouse and Zhang used Penner and Zeitlin's decorated super Teichm{\"u}ller theory to define a super version of the cluster algebra of type and gave a combinatorial formula to compute the even generators. We extend this theory by giving a homological way of explicitly computing these generators by defining a super CC-map for type .
Cite
@article{arxiv.2402.15495,
title = {Super Caldero--Chapoton map for type $A$},
author = {İlke Çanakçı and Francesca Fedele and Ana Garcia Elsener and Khrystyna Serhiyenko},
journal= {arXiv preprint arXiv:2402.15495},
year = {2024}
}
Comments
43 pages, 19 figures, This work originates as part of the WINART3 Workshop: Women in Noncommutative Algebra and Representation Theory