5 papers
Syzygy Transformations of Cluster Characters and Geometric Twists
Jiarui Fei
We use the full multiplication formula to study syzygy and suspension of cluster characters. In stably 2-Calabi--Yau Frobenius categories, syzygy and cosyzygy induce inverse automo…
Cluster Geometry of Universal Schubert Polynomials I: Geometric Bases and Schubert Transitions
Jiarui Fei
We study Fulton's universal Schubert polynomials as regular functions on the upper unitriangular group . The standard triangular cluster structure associate…
Schur Rank, Compatibility Degree, and Canonical Decomposition
Jiarui Fei
The notion of denominator vectors can be extended to all generic basis elements of upper cluster algebras in a natural way. Under a weakened version of generic pairing assumption,…
On AI's "semistable torsion classes and canonical decompositions"
Jiarui Fei
In this short note, we give two-line proofs for main results in "Semistable torsion classes and canonical decompositions" by Asai-Iyama from a main result in "Tropical -polynomi…
General Presentations of Algebras and Foundations of -tilting Theory
Harm Derksen, Jiarui Fei
In this short note, we explain how the main results in "-tilting theory" by Adachi-Iyama-Reiten follow from the results in Section 5 of "General presentations of algebras" by De…