Iterated Loop Algebras

On m-cluster tilted algebras and trivial extensions

In this work we study the connection between iterated tilted algebras and m-cluster tilted algebras. We show that an iterated tilted algebra induces an m-cluster tilted algebra. This m-cluster tilted algebra can be seen as a trivial extension of another iterated tilted algebra which is derived equivalent to the original one. We give a procedure to find this new iterated tilted algebra. These m-cluster tilted algebras are quotients of higher relation extensions.

From iterated tilted algebras to cluster-tilted algebras

In this paper the relationship between iterated tilted algebras and cluster-tilted algebras and relation-extensions is studied. In the Dynkin case, it is shown that the relationship is very strong and combinatorial.

A型迭代倾斜代数的枚举

Enumerating iterated tilted algebras in type $A$

该研究建立了A型$A_n$迭代倾斜代数同构类与凸$n+1$边形旋转等价非交叉生成树的双射关系，通过构造迭代倾斜代数与例外集的关联完成证明。

群环上的迭代Hopf Ore扩张

Iterated Hopf Ore Extensions over Group Rings

引入并研究群代数上的两步Ore扩张构造的一类Hopf代数，统一推广了广义Taft代数和与sl2相关的Hopf代数，分析了环论性质并分类了有限维单模。

Iterated torus knots and double affine Hecke algebras

We give a topological realization of the (spherical) double affine Hecke algebra $\mathrm{SH}_{q,t}$ of type $A_1$, and we use this to construct a module over $\mathrm{SH}_{q,t}$ for any knot $K \subset S^3$. As an application, we give a purely topological interpretation of Cherednik's 2-variable polynomials $P_n(r,s; q,t)$ of type $A_1$ from [Che13] (where $r,s \in \mathbb{Z}$ are relatively prime), and we give a new proof that these specialize to the colored Jones polynomials of the $r,s$ torus knot. We then generalize Cherednik's construction (for $\mathcal{sl}_2$) to all iterated cables of…

对称周期代数的迭代突变

Iterated mutations of symmetric periodic algebras

本文研究了对称周期代数的迭代突变，证明当顶点为d-周期性时，突变操作的阶数为d-2，并探讨了相关结论与示例。