The greedy basis equals the theta basis
arXiv:1508.01404 · doi:10.1016/j.jcta.2016.08.004
Abstract
We prove the equality of two canonical bases of a rank 2 cluster algebra, the greedy basis of Lee-Li-Zelevinsky and the theta basis of Gross-Hacking-Keel-Kontsevich.
arXiv comment17 pages
References in corpus (9)
- Semicanonical bases and preprojective algebras
- Graded quiver varieties, quantum cluster algebras and dual canonical basis
- Bases for cluster algebras from surfaces
- Universal geometric cluster algebras
- Combinatorial frameworks for cluster algebras
- Proof of the Kontsevich Non-Commutative Cluster Positivity Conjecture
- Mirror symmetry for P^2 and tropical geometry
- A tropical view on Landau-Ginzburg models
- The Feigin Tetrahedron
Cited by in corpus (14)
- Bases for cluster algebras from orbifolds
- Scattering fans
- A combinatorial approach to scattering diagrams
- Strong positivity for quantum theta bases of quantum cluster algebras
- Explicit equations for mirror families to log Calabi-Yau surfaces
- τ-Cluster Morphism Categories and Picture Groups
- Theta functions and quiver Grassmannians
- Cluster Algebras and Scattering Diagrams, Part II. Cluster Patterns and Scattering Diagrams
- On Generalized Minors and Quiver Representations
- From frieze patterns to cluster categories
- Dominance phenomena: mutation, scattering and cluster algebras
- Affine cluster monomials are generalized minors
- Theta bases are atomic
- Cluster algebras and their bases