Peigen Cao

collaborators

5 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 $Frac (S_{I ¨} (S))$ of the stated $SL_{n}$ -skein algebra ${\mathscr S}_Ï(\mathf…

math.RT2026

Additive categorification of the monoidal $I^$ -invariant

Ricardo Canesin, Peigen Cao, Geoffrey Janssens

In this paper, we contribute to the broad aim of relating invariants of additive and monoidal categorifications of cluster algebras. Specifically, in the setting of representations…

math.RT2026

Newton polytopes in cluster algebras and $I ¨ $ -tilting theory

Peigen Cao

We prove that the cluster monomials in non-initial cluster variables are uniquely determined by the Newton polytopes of their $F$ -polynomials for skew-symmetrizable cluster algebra…

math.RT2025

F-invariant and E-invariant

Peigen Cao

$F$ -invariant for a pair of good elements (e.g. cluster monomials) in cluster algebras is introduced by the author in a previous work. A key feature of $F$ -invariant is that it is…

math.RT2025

Modules determined by their Newton polytopes

Peigen Cao

In the $I ¨ $ -tilting theory, there exist two classes of foundamental modules: indecomposable $I ¨ $ -rigid modules and left finite bricks. In this paper, we prove the indecomposable $Ï…

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

Additive categorification of the monoidal I^-invariant

Newton polytopes in cluster algebras and I¨-tilting theory

F-invariant and E-invariant

Modules determined by their Newton polytopes

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

Additive categorification of the monoidal $I^$ -invariant

Newton polytopes in cluster algebras and $I ¨ $ -tilting theory