Local structure of tame symmetric algebras of period four
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913570474688512 |
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| author | Erdmann, Karin Hajduk, Adam Skowyrski, Adam |
| author_facet | Erdmann, Karin Hajduk, Adam Skowyrski, Adam |
| contents | In this paper we study the structure of Gabriel quivers of tame symmetric algebras of period four. More precisely, we focus on algebras having Gabriel quiver {\it biregular}, i.e. the numbers of arrows starting and ending at any vertex are equal, and do not exceed $2$. We describe the local structure of biregular Gabriel quivers of tame symmetric algebras of period four, including certain idempotent algebras. The main result of this paper shows that, in fact, these Gabriel quivers have local structure exactly as Gabriel quivers of so called {\it weighted surface algebras}, which partially extends known characterization of algebras of generalized quaternion type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_01235 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Local structure of tame symmetric algebras of period four Erdmann, Karin Hajduk, Adam Skowyrski, Adam Representation Theory In this paper we study the structure of Gabriel quivers of tame symmetric algebras of period four. More precisely, we focus on algebras having Gabriel quiver {\it biregular}, i.e. the numbers of arrows starting and ending at any vertex are equal, and do not exceed $2$. We describe the local structure of biregular Gabriel quivers of tame symmetric algebras of period four, including certain idempotent algebras. The main result of this paper shows that, in fact, these Gabriel quivers have local structure exactly as Gabriel quivers of so called {\it weighted surface algebras}, which partially extends known characterization of algebras of generalized quaternion type. |
| title | Local structure of tame symmetric algebras of period four |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2411.01235 |