Work

Super Caldero–Chapoton map for type A

Year: 2025

Type: article

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{ü}ller theory to define a super version of the cluster algebra of type $A$ 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 $A$.

Source: Journal of Algebra

DOI: 10.1016/j.jalgebra.2025.04.018

Authors: İlke Çanakçı, Francesca Fedele, Ana Garcia Elsener, Khrystyna Serhiyenko

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,310