Jacobian Algebras of Species with Potentials and 2-Representation Finite Algebras
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915535001747456 |
|---|---|
| author | Söderberg, Christoffer |
| author_facet | Söderberg, Christoffer |
| contents | We study $2$-representation finite $\mathbb{K}$-algebras obtained from tensor products of tensor algebras of species. In earlier work we computed the higher preprojective algebra of said algebras to be given as Jacobian algebras of certain species with potential $(S, W)$, which are self-injective and finite dimensional. Truncating these Jacobian algebras yields a rich source of $2$-representation finite $\mathbb{K}$-algebras. Under suitable assumptions, we prove that the set of all cuts of $(S, W)$ is transitive under successive cut-mutations. Furthermore, we show that cuts and cut-mutation correspond to truncated Jacobian algebras and $2$-APR tilting, respectively. Consequently, under certain assumptions, all truncated Jacobian algebras are related to each other via $2$-APR tilting. We produce various new examples of $2$-representation finite $\mathbb{K}$-algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_04865 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Jacobian Algebras of Species with Potentials and 2-Representation Finite Algebras Söderberg, Christoffer Representation Theory We study $2$-representation finite $\mathbb{K}$-algebras obtained from tensor products of tensor algebras of species. In earlier work we computed the higher preprojective algebra of said algebras to be given as Jacobian algebras of certain species with potential $(S, W)$, which are self-injective and finite dimensional. Truncating these Jacobian algebras yields a rich source of $2$-representation finite $\mathbb{K}$-algebras. Under suitable assumptions, we prove that the set of all cuts of $(S, W)$ is transitive under successive cut-mutations. Furthermore, we show that cuts and cut-mutation correspond to truncated Jacobian algebras and $2$-APR tilting, respectively. Consequently, under certain assumptions, all truncated Jacobian algebras are related to each other via $2$-APR tilting. We produce various new examples of $2$-representation finite $\mathbb{K}$-algebras. |
| title | Jacobian Algebras of Species with Potentials and 2-Representation Finite Algebras |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2510.04865 |