6 papers
Transferred -structures and a classification of binary brackets for finite-dimensional skew-gentle algebras
Zixu Li, Liyu Liu, Lingchao Meng
We construct a transferred -structure on the shifted Chouhy--Solotar cochain complex of a finite-dimensional skew-gentle algebra and give explicit basis-level formulas fo…
Lift-Free Approaches to Random Rotation Number and Numerical Approximation
Zixu Li, Simon Lloyd
We study the random rotation number for random circle homeomorphisms. We introduce two new definitions of the random rotation number that can be stated without reference to any cho…
Periodicity and Rotation Number for Random Circle Homeomorphisms
Zixu Li, Simon Lloyd
We study discrete-time random dynamical systems where each fibre map is an orientation-preserving homeomorphism of the circle. We prove that the existence of a random periodic cycl…
A cluster theory approach from mutation invariants to Diophantine equations
Zhichao Chen, Zixu Li
In this paper, we define and classify the sign-equivalent exchange matrices. We give a Diophantine explanation for the differences between rank 2 cluster algebras of finite type an…
A geometric realization of Koszul duality for graded gentle algebras
Zixu Li, Yu Qiu, Yu Zhou
We show that the Koszul functor of a homologically smooth graded gentle algebra can be realized as the half rotation in a geometric model. As a byproduct, we prove an intersection-…
Mutation invariants of cluster algebras of rank 2
Zhichao Chen, Zixu Li
We consider the mutation invariants of cluster algebras of rank 2. We characterize the mutation invariants of finite type. Two examples are provided for the affine type and we prov…