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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.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…
math.QA2024
Based cluster algebras of infinite rank
Fan Qin
We extend based cluster algebras from the finite rank case to the infinite rank case. By extending (quantum) cluster algebras whose initial seeds are associated with signed words (…