3 papers
math.QA2026
Integral cluster structures on quantized coordinate rings
Hironori Oya, Fan Qin, Milen Yakimov
We develop (quantum) cluster algebra structures over arbitrary commutative unital rings and prove that the (quantized) coordinate rings of connected simply-connected comple…
math.RT2025
An introduction to representation-theoretic canonical bases of cluster algebras
Fan Qin
This is an introduction to cluster algebras and their common triangular bases. These bases are Kazhdan-Lusztig-type and serve as the canonical bases of cluster algebras from the re…
math.QA2025
Partially compactified quantum cluster structures on simple algebraic groups and the full Berenstein--Zelevinsky conjecture
Fan Qin, Milen Yakimov
The construction of partially compactified cluster algebras on coordinate rings is handled by using codimension 2 arguments on cluster covers. An analog of this in the quantum situ…