Generalized weighted surface algebras
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2021
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866914104514445312 |
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| author | Skowroński, Andrzej Skowyrski, Adam |
| author_facet | Skowroński, Andrzej Skowyrski, Adam |
| contents | The weighted triangulation algebras associated to triangulation quivers and their socle deformations were recently introduced and studied in [15]-[20] and [2]. These algebras, based on surface triangulations and originated from the theory of cluster algebras, were also proved to be (with some minor exceptions) finite-dimensional tame symmetric and periodic algebras of period 4. In this paper, we introduce a new concept of a generalized triangulation quiver, extending the notion of a triangulation quiver. Inparticular, it is also shown that the generalized triangulation quivers can be constructed from triangulations of orientable surfaces with marked self-foldedtriangles. Moreover, motivated by the recent results of [28], we define and investigate so called weighted generalized triangulation algebras associated to generalized triangulation quivers, which naturally arise from mutations of weighted triangulation algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2106_15218 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Generalized weighted surface algebras Skowroński, Andrzej Skowyrski, Adam Representation Theory The weighted triangulation algebras associated to triangulation quivers and their socle deformations were recently introduced and studied in [15]-[20] and [2]. These algebras, based on surface triangulations and originated from the theory of cluster algebras, were also proved to be (with some minor exceptions) finite-dimensional tame symmetric and periodic algebras of period 4. In this paper, we introduce a new concept of a generalized triangulation quiver, extending the notion of a triangulation quiver. Inparticular, it is also shown that the generalized triangulation quivers can be constructed from triangulations of orientable surfaces with marked self-foldedtriangles. Moreover, motivated by the recent results of [28], we define and investigate so called weighted generalized triangulation algebras associated to generalized triangulation quivers, which naturally arise from mutations of weighted triangulation algebras. |
| title | Generalized weighted surface algebras |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2106.15218 |