Higher tetrahedral algebras
We introduce and study the higher tetrahedral algebras, an exotic family of finite-dimensional tame symmetric algebras over an algebraically closed field. The Gabriel quiver of such an algebra is the triangulation quiver associated to the coherent orientation of the tetrahedron. Surprisingly, these...
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| Format: | Journal article |
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Springer
2018
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| _version_ | 1826262426628128768 |
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| author | Erdmann, K Skowroński, A |
| author_facet | Erdmann, K Skowroński, A |
| author_sort | Erdmann, K |
| collection | OXFORD |
| description | We introduce and study the higher tetrahedral algebras, an exotic family of finite-dimensional tame symmetric algebras over an algebraically closed field. The Gabriel quiver of such an algebra is the triangulation quiver associated to the coherent orientation of the tetrahedron. Surprisingly, these algebras occurred in the classification of all algebras of generalized quaternion type, but are not weighted surface algebras. We prove that a higher tetrahedral algebra is periodic if and only if it is non-singular. |
| first_indexed | 2024-03-06T19:35:59Z |
| format | Journal article |
| id | oxford-uuid:1f101095-098b-427f-b7e1-c41f23579505 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T19:35:59Z |
| publishDate | 2018 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:1f101095-098b-427f-b7e1-c41f235795052022-03-26T11:19:49ZHigher tetrahedral algebrasJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:1f101095-098b-427f-b7e1-c41f23579505Symplectic Elements at OxfordSpringer2018Erdmann, KSkowroński, AWe introduce and study the higher tetrahedral algebras, an exotic family of finite-dimensional tame symmetric algebras over an algebraically closed field. The Gabriel quiver of such an algebra is the triangulation quiver associated to the coherent orientation of the tetrahedron. Surprisingly, these algebras occurred in the classification of all algebras of generalized quaternion type, but are not weighted surface algebras. We prove that a higher tetrahedral algebra is periodic if and only if it is non-singular. |
| spellingShingle | Erdmann, K Skowroński, A Higher tetrahedral algebras |
| title | Higher tetrahedral algebras |
| title_full | Higher tetrahedral algebras |
| title_fullStr | Higher tetrahedral algebras |
| title_full_unstemmed | Higher tetrahedral algebras |
| title_short | Higher tetrahedral algebras |
| title_sort | higher tetrahedral algebras |
| work_keys_str_mv | AT erdmannk highertetrahedralalgebras AT skowronskia highertetrahedralalgebras |