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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Legendrian knots and cluster algebras via augmentations
Legendarian结 簇代数 增广
2023/5/16
Legendrian knots and their exact Lagrangian fillings are central objects to study in low dimensional contact and symplectic topology. In recent developments, cluster algebras have proven to be powerfu...
International Workshop on Cluster Algebras and Related Topics
International Workshop Cluster Algebras and Related Topics
2017/2/15
The purposes of this conference are to discuss the structures and classifications of the cluster algebras of geometric type, the recent advances of several main conjectures of cluster theory, the conn...
Skein algebras and cluster algebras of marked surfaces
Skein algebras cluster algebras marked surfaces Quantum Algebra Geometric Topology
2012/4/17
This paper defines several algebras associated to an oriented surface S with a finite set of marked points on the boundary. The first is the skein algebra Sk_q(S), which is spanned by links in the sur...
Poisson Ideals in Cluster Algebras and the Spectra of Quantized Coordinate Rings
Poisson Ideals Cluster Algebras the Spectra of Quantized Coordinate Rings Quantum Algebra
2011/9/6
Abstract: We describe the Poisson ideals and attached symplectic geometry of a cluster algebra with compatible Poisson structure. We apply these results to determine the spectrum of a quantum cluster ...
The purpose of this chapter is to give an introduction to the theory of cluster categories and cluster-tilted algebras, with some background on the theory of cluster algebras, which motivated these to...
Difference equations and cluster algebras I: Poisson bracket for integrable difference equations
Difference equations cluster algebras Poisson bracket for integrable difference equations
2011/2/28
We introduce the cluster algebraic formulation of the integrable difference equations, the discrete Lotka-Volterra equation and the discrete Li-ouville equation, from the view point of the general T-s...
Let $A_{n}(S)$ be a coefficient free cluster algebra over a field $K$. A cluster automorphism is an element of $Aut._{K}K(t_{1}, t_{2},..., t_{n})$ which leaves the set of all cluster variables, $\xi_...
On the quantum cluster algebras of finite types
the quantum cluster algebras finite types
2010/11/12
We extend the definition of the quantum analogue of Caldero-Chapoton map defined by \cite{rupel}\cite{fanqin}. When $Q$ is a quiver of finite type, we prove that the algebra $\mathcal{AH}_{|k|}(Q)$ g...
Cluster algebras and representation theory
cluster algebra canonical and semicanonical basis preprojective algebra
2010/12/10
We apply the new theory of cluster algebras of Fomin and Zelevinsky to study some combinatorial problems arising in Lie theory. This is joint work with Geiss and Schr¨oer (§3, 4, 5, 6), and with Herna...
This paper investigates the Poisson geometry associate to a cluster algebra over the complex numbers, and its relationship to compatible torus actions.