







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 $\mc{X}$-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.
此内容由惯性聚合(RSS阅读器)自动聚合整理,仅供阅读参考。 原文来自 — 版权归原作者所有。