arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2602.16593math.QAmath-phmath.FAmath.MP
收藏

收敛扭转变形

Convergent Twist Deformations

Università degli Studi di Salerno（萨莱诺大学）；University of Würzburg（维尔茨堡大学）

Chiara Esposito, Michael Heins, Stefan Waldmann

备注：
42 pages, updated bibliography
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

AI总结：

本文通过建立函子框架，证明了Drinfeld扭在解析向量空间上的收敛性，并应用于Giaquinto和Zhang构造的扭，确定了解析向量空间并回答了严格版本的可能性问题。

摘要：

本文建立了一个关于Drinfeld的通用变形公式（UDF）在解析向量空间上收敛的函子框架。这通过将后者顺序与变形下的Drinfeld扭的等连续条件相匹配来实现。在整个过程中，我们考虑有限维李代数在局部凸空间上的连续线性映射的表示。这使我们不仅能够建立形式幂级数的收敛性，还能建立变形的双线性映射的连续性以及整个关于变形参数ℏ的全解析依赖性。最后，我们通过将其应用于Giaquinto和Zhang明确构造的Drinfeld扭，证明了我们的理论的有效性，其中我们既建立了等连续条件，又确定了具体的表示对应的解析向量空间。从而回答了Giaquinto和Zhang提出的问题，即他们的正式扭是否有可能在正数范围内严格成立。

英文摘要：

This paper establishes a functorial framework for convergence of Drinfeld's Universal Deformation Formula (UDF) on spaces of analytic vectors. This is accomplished by matching the order of the latter with an equicontinuity condition on the Drinfeld twist underlying the deformation. Throughout, we work with representations of finite-dimensional Lie algebras by continuous linear mappings on locally convex spaces. This allows us to establish not only convergence of the formal power series, but the continuity of the deformed bilinear mappings as well as the entire holomorphic dependence on the deformation parameter $\hbar$. Finally, we demonstrate the effectiveness of our theory by applying it to the explicit Drinfeld twists constructed by Giaquinto and Zhang, where we establish both the equicontinuity condition and determine the corresponding spaces of analytic vectors for concrete representations. Thereby we answer a question posed by Giaquinto and Zhang whether a strict version of their formal twists is possible in the positive.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

↑