sl（3）的Character环的扩张及其量化

A 2-categorical extension of Etingof-Kazhdan quantisation

Let k be a field of characteristic zero. Etingof and Kazhdan constructed a quantisation U_h(b) of any Lie bialgebra b over k, which depends on the choice of an associator Phi. They prove moreover that this quantisation is functorial in b. Remarkably, the quantum group U_h(b) is endowed with a Tannakian equivalence F_b from the braided tensor category of Drinfeld-Yetter modules over b, with deformed associativity constraints given by Phi, to that of Drinfeld-Yetter modules over U_h(b). In this paper, we prove that the equivalence F_b is functorial in b.

通过表示论的聚类结构：聚类集合、热带对偶性、聚类特征和量化

Cluster structures via representation theory: cluster ensembles, tropical duality, cluster characters and quantisation

本文通过表示论发展聚类结构理论，结合热带对偶性和量子化，揭示聚类集合与特征的范畴化方法及应用。

On the universal character ring and the character variety of the (-2,3,2n+1)-pretzel knot

We calculate the universal character ring of a class of two-generator, one-relator groups. As an application we give a less technical proof of a result in [LT] on the universal character ring of the (-2,3,2n+1)-pretzel knot. We also give an elementary proof of a result in [Ma] on the character variety of the (-2,3,2n+1)-pretzel knot.

The universal character ring of the (-2,2m+1,2n)-pretzel link

We explicitly calculate the universal character ring of the (-2,2m+1,2n)-pretzel link and show that it is reduced for all integers m and n.

The universal character ring of some families of one-relator groups

We study the universal character ring of some families of one-relator groups. As an application, we calculate the universal character ring of two-generator one-relator groups whose relators are palindrome, and, in particular, of the (-2,2m+1,2n+1)-pretzel knot for all integers m and n. For the (-2,3,2n+1)-pretzel knot, we give a less technical proof of a result in [LT1] on its universal character ring, and an elementary proof of a result in [Ma] on the number of irreducible components of its character variety.

具有$SL_2({\mathbb C})$ -特征标的环与Kauffman-Skein模

Rings of $SL_2({\mathbb C})$-Characters and the Kauffman Bracket Skein Module

设$M$是紧致可定向三维流形. $M$的基本群的$SL_2({\mathbb C})$表示的特征标的集合形成闭仿射代数集合。我们证明了它的坐标环同构于Kauffman括号skein模的一个特殊化。这是通过将模块制作成环的组合模拟来实现的，其中利用绞链理论的工具来阐明字符之间的关系。最后，我们的应用程序，证明了一个小流形的专门模块必然是有限维的。