Towards reconstruction of finite tensor categories
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909467132559360 |
|---|---|
| author | Jubeir, Mitchell Wang, Zhenghan |
| author_facet | Jubeir, Mitchell Wang, Zhenghan |
| contents | We take a first step towards a reconstruction of finite tensor categories using finitely many $F$-matrices. The goal is to reconstruct a finite tensor category from its projective ideal. Here we set up the framework for an important concrete example--the $8$-dimensional Nicholas Hopf algebra $K_2$. Of particular importance is to determine its Green ring and tensor ideals. The Hopf algebra $K_2$ allows the recovery of $(2+1)$-dimensional Seiberg-Witten TQFT from Hennings TQFT based on $K_2$. This powerful result convinced us that it is interesting to study the Green ring of $K_2$ and its tensor ideals in more detail. Our results clearly illustrate the difficulties arisen from the proliferation of non-projective reducible indecomposable objects in finite tensor categories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_03987 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Towards reconstruction of finite tensor categories Jubeir, Mitchell Wang, Zhenghan Quantum Algebra We take a first step towards a reconstruction of finite tensor categories using finitely many $F$-matrices. The goal is to reconstruct a finite tensor category from its projective ideal. Here we set up the framework for an important concrete example--the $8$-dimensional Nicholas Hopf algebra $K_2$. Of particular importance is to determine its Green ring and tensor ideals. The Hopf algebra $K_2$ allows the recovery of $(2+1)$-dimensional Seiberg-Witten TQFT from Hennings TQFT based on $K_2$. This powerful result convinced us that it is interesting to study the Green ring of $K_2$ and its tensor ideals in more detail. Our results clearly illustrate the difficulties arisen from the proliferation of non-projective reducible indecomposable objects in finite tensor categories. |
| title | Towards reconstruction of finite tensor categories |
| topic | Quantum Algebra |
| url | https://arxiv.org/abs/2501.03987 |