A_n-R表示的循环对称性

The singularity and cosingularity categories of $C^*BG$ for groups with cyclic Sylow $p$-subgroups

We construct a differential graded algebra (DGA) modelling certain $A_\infty$ algebras associated with a finite group $G$ with cyclic Sylow subgroups, namely $H^*BG$ and $H_*ΩBG^{^\wedge}_p$. We use our construction to investigate the singularity and cosingularity categories of these algebras. We give a complete classification of the indecomposables in these categories, and describe the Auslander--Reiten quiver. The theory applies to Brauer tree algebras in arbitrary characteristic, and we end with an example in characteristic zero coming from the Hecke algebras of symmetric groups.

弦图的循环对称性

Cyclic Symmetries of Chord Diagrams

本文通过直接证明，将Proalgebraic graded Grothendieck-Teichmüller群与基于Furusho对五边形方程的循环括号弦图prounipotent循环操作符的自同构群证明同构，并描述了该群对带状弦图范畴的作用。

循环操作符与结的Grothendieck-Teichmüller对称性

Grothendieck-Teichmüller Symmetries of Cyclic Operads and Tangles

本文研究了循环操作符与结的Grothendieck-Teichmüller对称性，通过操作符模型揭示了 profinite 结的算术对称性，并给出了形式性的另一种证明。

循环神经的对称性

Symmetries of the cyclic nerve

本研究以因子化同调视角系统研究$(\n,1)$-范畴的循环神经即Hochschild同调，通过箭图表示编码范畴，识别其对称性并构造非稳定循环迹映射，统一三类循环范畴，给出$n=1$因子化同调的组合描述。