9 papers
Partial -invariants and cluster categorifications
Peigen Cao, Ryo Fujita, Kota Murakami
The -invariant in cluster algebras is a combinatorial invariant that unifies the -invariant from additive categorification and the -invariant from monoidal cate…
Linear independence of global monomials on positive spaces
Peigen Cao
In this paper, we prove that global monomials on positive spaces are linearly independent, extending the basic fact that Laurent monomials in a Laurent polynomial algebra are linea…
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…
Additive categorification of the monoidal -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…
Newton polytopes in cluster algebras and -tilting theory
Peigen Cao
We prove that the cluster monomials in non-initial cluster variables are uniquely determined by the Newton polytopes of their -polynomials for skew-symmetrizable cluster algebra…
F-invariant and E-invariant
Peigen Cao
-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 -invariant is that it is…
Modules determined by their Newton polytopes
Peigen Cao
In the -tilting theory, there exist two classes of foundamental modules: indecomposable -rigid modules and left finite bricks. In this paper, we prove the indecomposable -…
Tropical friezes and cluster-additive functions via Fock-Goncharov duality and a conjecture of Ringel
Peigen Cao, Antoine de Saint Germain, Jiang-Hua Lu
We study tropical friezes and cluster-additive functions associated to symmetrizable generalized Cartan matrices in the framework of Fock-Goncharov duality in cluster algebras. In…
Tropical friezes and cluster-additive functions via Fock-Goncharov duality and a conjecture of Ringel
Peigen Cao, Antoine de Saint Germain, Jiang-Hua Lu
We study tropical friezes and cluster-additive functions associated to symmetrizable generalized Cartan matrices in the framework of Fock-Goncharov duality in cluster algebras. In…