Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2204.06418 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917955124592640 |
|---|---|
| author | Wang, Qi Zhang, Yingying |
| author_facet | Wang, Qi Zhang, Yingying |
| contents | We show that trivial extensions of gentle tree algebras are exactly Brauer tree algebras without exceptional vertex. We also give a characterization for the algebras whose trivial extensions are Brauer line/star/cycle algebras. As a consequence, the number of support $τ$-tilting modules over the trivial extension $T(A)$ of a gentle tree algebra $A$ depends only on the number of simple $A$-modules. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_06418 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On $τ$-tilting modules over trivial extensions of gentle tree algebras Wang, Qi Zhang, Yingying Representation Theory We show that trivial extensions of gentle tree algebras are exactly Brauer tree algebras without exceptional vertex. We also give a characterization for the algebras whose trivial extensions are Brauer line/star/cycle algebras. As a consequence, the number of support $τ$-tilting modules over the trivial extension $T(A)$ of a gentle tree algebra $A$ depends only on the number of simple $A$-modules. |
| title | On $τ$-tilting modules over trivial extensions of gentle tree algebras |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2204.06418 |