Laurent phenomenon algebras

By Thomas Lam, Pavlo Pylyavskyy. 2012

79 citations recorded by the source corpus.

We generalize Fomin and Zelevinsky's cluster algebras by allowing exchange polynomials to be arbitrary irreducible polynomials, rather than binomials.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/844a3b264415439242eb4a44b52a9a9fd1a36cc0

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. P. Hacking
2. S. Keel
3. Mark Gross
4. David E. Speyer
5. Thomas Lam
6. Eric Katz
7. Mark Shimozono
8. Dhruv Ranganathan

In Computational Theory and Mathematics

1. P. Hacking
2. S. Keel
3. Mark Gross
4. David E. Speyer
5. Thomas Lam
6. Eric Katz
7. Bernd Sturmfels
8. Jenia Tevelev

In Geometry and Topology

1. P. Hacking
2. S. Keel
3. Mark Gross
4. David E. Speyer
5. Thomas Lam
6. Bernd S Siebert
7. Jenia Tevelev
8. Eric Katz

Citations in the corpus

• Birational geometry of cluster algebras (2013, methodology): “ry transform gives a mutation of a toric model in the same way, but the formulae for how the centers change are more complicated. For a general center, we checked one obtains the mutation formulae of [LP12]. In this note we restrict our treatment to the cluster variety case, as it is simpler and suffi”
• Cohomology of cluster varieties, I: Locally acyclic case (2016, background): “on 1 each. If r6= 0 , then this isotypic component is one-dimensional, in degree (2,(1,1)). Remark 7.4. The first author and Pylyavskyy have generalized cluster algebras to Laurent phenomenon algebras [LP]. The Laurent phenomenon algebra which plays the role analogous to xx′ = yb +1 (with y6= 0 ) is ”