2023/09/15 by Jiarui Fei, Fei, Jiarui
Computer Science · Mathematics · #16G10 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Matrix Theory and Algorithms #Primary 13F60 #Representation Theory (math.RT) #Rings and Algebras (math.RA) #Secondary 05E10
paper · pdf · doi:10.48550/arxiv.2309.08326
openalex publication_date 2023/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We describe the upper seminormal crystal structure for the μ-supported δ-vectors for any quiver with potential with reachable frozen vertices, or equivalently for the tropical points of the corresponding cluster \mcX-variety. We show that the crystal structure can be algebraically lifted to the generic basis of the upper cluster algebra. This can be viewed as an additive categorification of the crystal structure arising from cluster algebras. We introduce the biperfect bases in the cluster algebra setting and give a description of all biperfect bases, which are parametrized by lattice points in a product of polyhedral sets. We illustrate this theory from classical examples and new examples.