An expansion formula for type A and Kronecker quantum cluster algebras

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:171

Article

Canakci, Ilke¹  Lampe, Philipp² 

[1] Vrije Univ, Dept Math, NL-1081 HV Amsterdam, Netherlands

[2] SMSAS, Canterbury CT2 7FS, Kent, England

关键词: Quantum cluster algebras;    Non-commutative rings;    Surface cluster algebras;    Triangulations;    Arcs;    Snake graphs;    Perfect matchings;    Lattices;    Stembridge phenomenon;    Mathematical physics;   

DOI  :  10.1016/j.jcta.2019.105132

来源: Elsevier

【 摘 要 】

We introduce an expansion formula for elements in quantum cluster algebras associated to type A and Kronecker quivers with principal quantization. Our formula is parametrized by perfect matchings of snake graphs as in the classical case. In the Kronecker type, the coefficients are q-powers whose exponents are given by a weight function induced by the lattice of perfect matchings. As an application, we prove that a reflectional symmetry on the set of perfect matchings satisfies Stembridge's q = -1 phenomenon with respect to the weight function. Furthermore, we discuss a relation of our expansion formula to generating functions of BPS states. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free