Snake graph calculus and cluster algebras from surfaces II: self-crossing snake graphs

I Canakci, R Schiffler - Mathematische Zeitschrift, 2015 - Springer
Snake graphs appear naturally in the theory of cluster algebras. For cluster algebras from
surfaces, each cluster variable is given by a formula whose terms are parametrized by the …

[HTML][HTML] Extensions in Jacobian algebras and cluster categories of marked surfaces

I Canakci, S Schroll - Advances in Mathematics, 2017 - Elsevier
In the context of representation theory of finite dimensional algebras, string algebras have
been extensively studied and most aspects of their representation theory are well …

Snake graph calculus and cluster algebras from surfaces III: Band graphs and snake rings

İ Çanakçı, R Schiffler - International Mathematics Research …, 2019 - academic.oup.com
We introduce several commutative rings, the snake rings, that have strong connections to
cluster algebras and that are interesting on their own right as combinatorially defined rings …

[HTML][HTML] An expansion formula for type A and Kronecker quantum cluster algebras

İ Çanakçı, P Lampe - Journal of Combinatorial Theory, Series A, 2020 - Elsevier
We introduce an expansion formula for elements in quantum cluster algebras associated to
type A and Kronecker quivers with principal quantization. Our formula is parametrized by …

[HTML][HTML] Infinite rank surface cluster algebras

İ Çanakçı, A Felikson - Advances in Mathematics, 2019 - Elsevier
We generalise surface cluster algebras to the case of infinite surfaces where the surface
contains finitely many accumulation points of boundary marked points. To connect different …

Bases for cluster algebras from orbifolds with one marked point

İ Çanakçı, P Tumarkin - Algebraic Combinatorics, 2019 - numdam.org
Bases for cluster algebras from orbifolds with one marked point Page 1 ALGEBRAIC
COMBINATORICS Ilke Çanakçı & Pavel Tumarkin Bases for cluster algebras from orbifolds …