规范化泽塔发电机:基因型零和基因型一
Daniele Dorigoni1, Mehregan Doroudiani2, Joshua Drewitt3
1Centre for Particle Theory and Department of Mathematical Sciences, Durham University, Lower Mountjoy, Stockton Road, Durham, DH1 3LE UK.
Communications in mathematical physics
|December 11, 2025
概括
这项研究引入了zeta生成器,将里曼zeta值与里曼表面的李代数结构联系起来. 它为动态多zeta值建立了正规的同态性,并解决了属性为一的zeta生成器中的模糊性.
科学领域:
- 数学理论 数学理论
- 代数几何几何学的几何学
- 数学物理 数学物理
背景情况:
- 泽塔生成器是与奇数里曼泽塔值相关的导数.
- 它们作用于里曼表面基本组的李代数.
- 类零泽塔生成器是Ihara衍生,与Drinfeld关联器相关.
研究的目的:
- 描述正规的李多项式及其非李对应的特征.
- 提出一个规范的等态,将动态的多zeta值映射到f-字母表中.
- 用表示理论来解决属性一的泽塔生成器中的模两可.
主要方法:
- 通过形式和动机的多zeta值的双空间进行表征.
- 从类零设置到类一个建立正规的李多项式.
- 用Tsunogai的几何衍生来扩展一个类型的泽塔发生器.
- 强加一个表示理论条件来解决模两可.
主要成果:
- 规范多项式及其非Lie对应的特征.
- 建议在动态多zeta值和f-字母之间提出一个正规的等态.
- 确定属一中的正规的泽塔发生器,作用于圆的关联器.
- 一个类型的zeta生成器被系统地扩展,产生了明确的高阶计算.
- 解决了属性一的泽塔生成器的非几何部分的模糊性.
结论:
- 这项工作揭示了基因零和基因一泽塔发生器之间的紧密相互作用.
- 这种连接有助于在球上构造单值的多重多边数.
- 它链接到模块化图形形式的代-艾森斯坦-整体表示.
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