Double-bosonization and Majid's conjecture (V): grafting of quantum groups
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866914308654366720 |
|---|---|
| author | Hu, Hongmei Hu, Naihong |
| author_facet | Hu, Hongmei Hu, Naihong |
| contents | This paper aims to develop a grafting method to address Majid's conjecture, which enables the construction of a larger target quantum group by grafting two given smaller ones. This method is significant for advancing the understanding of the generation, classification, and construction of (quasi-)Hopf algebras. To pave the way for the grafting method, we first set up a multi-tensor product theory for generalized double-bosonization to acquire the necessary information on the braiding $R$-matrices (see \cite{HH2}). Beyond the perspective of braided monoidal categories arising from the representations of quantum subgroups, the grafting procedure necessitates incorporating structural information from root systems in Lie theory. This approach provides a one-stop strategy for resolving the generation problem in Majid's conjecture on quantum trees. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_18243 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Double-bosonization and Majid's conjecture (V): grafting of quantum groups Hu, Hongmei Hu, Naihong Quantum Algebra Mathematical Physics Representation Theory This paper aims to develop a grafting method to address Majid's conjecture, which enables the construction of a larger target quantum group by grafting two given smaller ones. This method is significant for advancing the understanding of the generation, classification, and construction of (quasi-)Hopf algebras. To pave the way for the grafting method, we first set up a multi-tensor product theory for generalized double-bosonization to acquire the necessary information on the braiding $R$-matrices (see \cite{HH2}). Beyond the perspective of braided monoidal categories arising from the representations of quantum subgroups, the grafting procedure necessitates incorporating structural information from root systems in Lie theory. This approach provides a one-stop strategy for resolving the generation problem in Majid's conjecture on quantum trees. |
| title | Double-bosonization and Majid's conjecture (V): grafting of quantum groups |
| topic | Quantum Algebra Mathematical Physics Representation Theory |
| url | https://arxiv.org/abs/2601.18243 |