Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.16593 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915827010240512 |
|---|---|
| author | Esposito, Chiara Heins, Michael Waldmann, Stefan |
| author_facet | Esposito, Chiara Heins, Michael Waldmann, Stefan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_16593 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Convergent Twist Deformations Esposito, Chiara Heins, Michael Waldmann, Stefan Quantum Algebra Mathematical Physics Functional Analysis 53D55, 46H35, 46L67 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. |
| title | Convergent Twist Deformations |
| topic | Quantum Algebra Mathematical Physics Functional Analysis 53D55, 46H35, 46L67 |
| url | https://arxiv.org/abs/2602.16593 |