Gentle algebras arising from surfaces with orbifold points of order 3, Part I: scattering diagrams

D Labardini-Fragoso, L Mou - Algebras and Representation Theory, 2024 - Springer
To each triangulation of any surface with marked points on the boundary and orbifold points
of order three, we associate a quiver (with loops) with potential whose Jacobian algebra is …

Scattering diagrams, tight gradings, and generalized positivity

A Burcroff, K Lee, L Mou - arXiv preprint arXiv:2409.15235, 2024 - arxiv.org
In 2013, Lee, Li, and Zelevinsky introduced combinatorial objects called compatible pairs to
construct the greedy bases for rank-2 cluster algebras, consisting of indecomposable …

Dilogarithm identities in cluster scattering diagrams

T Nakanishi - Nagoya Mathematical Journal, 2024 - cambridge.org
We extend the notion of y-variables (coefficients) in cluster algebras to cluster scattering
diagrams (CSDs). Accordingly, we extend the dilogarithm identity associated with a period in …

[PDF][PDF] OBERWOLFACH ARBEITSGEMEINSCHAFT: CLUSTER ALGEBRAS

Background. Cluster algebras, invented [FZ02] by Sergey Fomin and Andrei Zelevinsky
around the year 2000, are commutative algebras whose generators, the cluster variables …

Scattering diagrams for generalized cluster algebras

L Mou - Algebra & Number Theory, 2024 - msp.org
We construct scattering diagrams for Chekhov–Shapiro generalized cluster algebras where
exchange polynomials are factorized into binomials, generalizing the cluster scattering …