Algebras of generalized quaternion type: biregular case
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866918391222108160 |
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| author | Erdmann, Karin Hajduk, Adam Skowyrski, Adam |
| author_facet | Erdmann, Karin Hajduk, Adam Skowyrski, Adam |
| contents | This paper provides the next step towards classification of algebras of generalized quaternion type. Previously algebras with 2-regular Gabriel quiver were classified (a quiver is 2-regular if at each vertex, two arrows start and two arrows end). Here we classify the algebras where at each vertex, either one arrow starts and one arrow ends, or else two arrows start and two arrows end. Our main result shows that that any such algebra (up to socle equivalence) is either a weighted surface algebra, or a higher spherical algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_15086 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Algebras of generalized quaternion type: biregular case Erdmann, Karin Hajduk, Adam Skowyrski, Adam Representation Theory 16D50, 16E30, 16G20, 16G60 This paper provides the next step towards classification of algebras of generalized quaternion type. Previously algebras with 2-regular Gabriel quiver were classified (a quiver is 2-regular if at each vertex, two arrows start and two arrows end). Here we classify the algebras where at each vertex, either one arrow starts and one arrow ends, or else two arrows start and two arrows end. Our main result shows that that any such algebra (up to socle equivalence) is either a weighted surface algebra, or a higher spherical algebra. |
| title | Algebras of generalized quaternion type: biregular case |
| topic | Representation Theory 16D50, 16E30, 16G20, 16G60 |
| url | https://arxiv.org/abs/2603.15086 |