A quantum analogue of generic bases for affine cluster algebras
Ming Ding, Fan Xu
TL;DR
This paper develops quantum analogues of generic bases for finite and affine cluster algebras, providing a quantized framework that specializes to classical bases when parameters are set to 1.
Contribution
It introduces quantized generic bases for affine and finite type cluster algebras, extending classical concepts into the quantum setting.
Findings
Constructed quantum generic bases for finite and affine types.
Bases specialize to classical generic bases when q and coefficients are set to 1.
Provides a new quantum perspective on cluster algebra bases.
Abstract
We construct quantized versions of generic bases in quantum cluster algebras of finite and affine types. Under the specialization of and coefficients to 1, these bases are generic bases of finite and affine cluster algebras.
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