An introduction to Graph LP algebras
Laurent Phenomenon (LP) algebras are a generalization of cluster algebras introduced by Lam and Pylyavskyy. These algebras are known to have the Laurent Phenomenon, but positivity remains conjectural. Graph LP algebras are a subclass of LP algebras that have a concrete combinatorial encoding in terms of graphs. We will define Graph LP algebras, explore concrete examples, and demonstrate that Graph LP algebras defined by path graphs are, in fact, ordinary cluster algebras of type A. The material in this talk is intended to provide background for a subsequent talk on progress towards positivity.
