The greedy basis equals the theta basis
Man Wai Cheung, Mark Gross, Greg Muller, Gregg Musiker, Dylan Rupel,, Salvatore Stella, Harold Williams
TL;DR
This paper proves that two important canonical bases in rank 2 cluster algebras, the greedy basis and the theta basis, are actually the same, unifying two previously distinct concepts.
Contribution
It establishes the equality of the greedy and theta bases in rank 2 cluster algebras, clarifying their relationship and simplifying the understanding of these bases.
Findings
Proves the equality of the greedy and theta bases in rank 2 cluster algebras.
Unifies two canonical bases, simplifying their theoretical framework.
Provides a foundational result for further studies in cluster algebra bases.
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.