8 papers
Quantum cluster algebra realization for stated -skein algebras and rotation-invariant bases for polygons
Peigen Cao, Min Huang, Zhihao Wang
We construct a quantum cluster structure on the skew-field of fractions of the stated -skein algebra ${\mathscr S}_ω(\mathfra…
A mutation invariant for skew-symmetrizable matrices
Min Huang, Qiling Ma
Matrix mutation of skew-symmetrizable matrices is foundational in cluster algebra theory. Effective mutation invariants are essential for determining whether two matrices lie in th…
Quantum cluster realization for projected stated -skein algebras
Min Huang, Zhihao Wang
We introduce a quantum cluster algebra structure inside the skew-field fractions of the…
Noncommutative marked surfaces II: tagged triangulations, clusters, and their symmetries
Arkady Berenstein, Min Huang, Vladimir Retakh
The aim of the paper is to define noncommutative cluster structure on several algebras related to marked surfaces possibly with orbifold points of various orders, wh…
A Representation theoretic perspective of Koszul theory
Ales Bouhada, Min Huang, Zetao Lin +1
We discover a new connection between Koszul theory and representation theory. Let $\La$ be a quadratic algebra defined by a locally finite quiver with relations. Firstly, we give a…
Positivity for quantum cluster algebras from orbifolds
Min Huang
Let be a marked orbifold with or without punctures and let be a quantum cluster algebra from with arbitrary coefficients and quantization. We pro…
Last fall degree of semi-local polynomial systems
Ming-Deh A. Huang
We study the last fall degrees of {\em semi-local} polynomial systems, and the computational complexity of solving such systems for closed-point and rational-point solutions, where…
Friezes of cluster algebras of geometric type
Antoine de Saint Germain, Min Huang, Jiang-Hua Lu
For a cluster algebra over of geometric type, a of is defined to be a -algebra homomorphism from $\mathcal{A}…