Zhihao Wang

activity

20232026

S L_{n}

-skein modules, roots of unity, and TQFT

1 citations · 2 across the 11 of their papers we have counts for

collaborators

11 papers

math.QA2026

Quantum cluster algebra realization for stated $SL_{n}$ -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 $Frac (S_{ω} (S))$ of the stated $SL_{n}$ -skein algebra ${\mathscr S}_ω(\mathfra…

math.GT2026

Coordinates for $SL_{3}$ -web basis elements in closed surfaces

Zhe Sun, Zhihao Wang

The $SL_{3}$ -skein algebra of a closed surface $Σ_{g}$ is a quantization of the $SL_{3}$ character variety of $Σ_{g}$ , where $g$ denotes the genus of the surface. This algebra…

math.QA2025

Centers and representations of $SL_{n}$ quantum Teichmüller spaces

Zhihao Wang

In this paper, we compute the center of the balanced Fock-Goncharov algebra and determine its rank over the center when the quantum parameter is a root of unity. These results have…

math.QA2025

Quantum cluster realization for projected stated $SL_{n}$ -skein algebras

Min Huang, Zhihao Wang

We introduce a quantum cluster algebra structure $A_{ω} (S)$ inside the skew-field fractions $Frac (S_{ω} (S))$ of the…

math.GT2025

Frobenius homomorphisms for stated $SL_{n}$ -skein modules

Hyun Kyu Kim, Thang T. Q. Lê, Zhihao Wang

The stated $SL_{n}$ -skein algebra $S_{q^} (S)$ of a surface $S$ is a quantization of the $SL_{n}$ -character variety, and is spanned over…

math.QA2024

Naturality of $SL_{n}$ quantum trace maps for surfaces

Hyun Kyu Kim, Zhihao Wang

The $SL_{n}$ -skein algebra of a punctured surface $S$ , studied by Sikora, is an algebra generated by isotopy classes of $n$ -webs living in the thickened surface $\ma…

math.QA2024

The Unicity Theorem and the center of the $SL_{3}$ -skein algebra

Hyun Kyu Kim, Zhihao Wang

The $SL_{3}$ -skein algebra $S_{q ˉ} (S)$ of a punctured oriented surface $S$ is a quantum deformation of the coordinate algebra of the ${\rm…

math.GT2024

The classical limit for stated $S L_{n}$ -skein modules

Zhihao Wang

Let $(M, N)$ be a marked 3-manifold. We use $S_{n} (M, N, v)$ to denote the stated $S L_{n}$ -skein module of $(M, N)$ where $v$ is a nonzero complex number. We…

math.QA2024★ 1 cited

Stated $S L_{n}$ -skein modules, roots of unity, and TQFT

Zhihao Wang

For a pb surface $Σ$ , two positive integers $m, n$ with $m ∣ n$ , and two invertible elements $v, ε$ in a commutative domain $R$ with $ε^{2 m} = 1$ , we construct an $R$ -linear isomor…

math.QA2023★ 1 cited

Representation-reduced stated skein modules and algebras

Zhihao Wang

For any marked three manifold $(M, N)$ and any quantum parameter $q^{\frac{1}{2}}$ (a nonzero complex number), we use $S_{q^{1/2}} (M, N)$ to denote the s…

math.AG2023

Finiteness and dimension of stated skein modules over Frobenius

Zhihao Wang

When the quantum parameter $q^{1/2}$ is a root of unity of odd order. The stated skein module $S_{q^{1/2}} (M, N)$ has an $S_{1} (M, N)$ -module structure, where $(M…

Quantum cluster algebra realization for stated SLn​-skein algebras and rotation-invariant bases for polygons

Coordinates for SL3​-web basis elements in closed surfaces

Centers and representations of SLn​ quantum Teichmüller spaces

Quantum cluster realization for projected stated SLn​-skein algebras

Frobenius homomorphisms for stated SLn​-skein modules

Naturality of SLn​ quantum trace maps for surfaces

The Unicity Theorem and the center of the SL3​-skein algebra

The classical limit for stated SLn​-skein modules

Stated SLn​-skein modules, roots of unity, and TQFT

Representation-reduced stated skein modules and algebras

Finiteness and dimension of stated skein modules over Frobenius

Quantum cluster algebra realization for stated $SL_{n}$ -skein algebras and rotation-invariant bases for polygons

Coordinates for $SL_{3}$ -web basis elements in closed surfaces

Centers and representations of $SL_{n}$ quantum Teichmüller spaces

Quantum cluster realization for projected stated $SL_{n}$ -skein algebras

Frobenius homomorphisms for stated $SL_{n}$ -skein modules

Naturality of $SL_{n}$ quantum trace maps for surfaces

The Unicity Theorem and the center of the $SL_{3}$ -skein algebra

The classical limit for stated $S L_{n}$ -skein modules

Stated $S L_{n}$ -skein modules, roots of unity, and TQFT