A construction of simple-minded systems over domestic Brauer graph algebras I: the 2-domestic case
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914066703843328 |
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| author | Zhang, Zhen |
| author_facet | Zhang, Zhen |
| contents | Let $A$ be a 2-domestic Brauer graph algebra. We present a construction for a family of objects on $A$-$\stmod$ to be a simple-minded system and our construction provides all simple-minded systems on $A$-$\stmod$. As a byproduct, we provide a new proof of AR-conjecture for 2-domestic Brauer graph algebras and we prove that a weakly simple-minded system with a finite cardinality is a simple-minded system on $A$-$\stmod$. We also prove that an orthogonal system $\mathcal{S}$ which contains at least one object for an Euclidean component extends to a simple-minded system on $A$-$\stmod$ and its extension closure $\mathcal{F}(\mathcal{S})$ is functorially finite. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_24184 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A construction of simple-minded systems over domestic Brauer graph algebras I: the 2-domestic case Zhang, Zhen Representation Theory Let $A$ be a 2-domestic Brauer graph algebra. We present a construction for a family of objects on $A$-$\stmod$ to be a simple-minded system and our construction provides all simple-minded systems on $A$-$\stmod$. As a byproduct, we provide a new proof of AR-conjecture for 2-domestic Brauer graph algebras and we prove that a weakly simple-minded system with a finite cardinality is a simple-minded system on $A$-$\stmod$. We also prove that an orthogonal system $\mathcal{S}$ which contains at least one object for an Euclidean component extends to a simple-minded system on $A$-$\stmod$ and its extension closure $\mathcal{F}(\mathcal{S})$ is functorially finite. |
| title | A construction of simple-minded systems over domestic Brauer graph algebras I: the 2-domestic case |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2509.24184 |