Skew-Brauer graph algebras
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866908667760082944 |
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| author | Elsener, Ana García Guazzelli, Victoria Valdivieso, Yadira |
| author_facet | Elsener, Ana García Guazzelli, Victoria Valdivieso, Yadira |
| contents | In this work, we introduce a new class of algebras called skew-Brauer graph algebras, which generalize the well-known Brauer graph algebras. We establish that skew-Brauer graph algebras are symmetric and can be defined using a Brauer graph with additional information. We show that the class of trivial extensions of skew-gentle algebras coincides with a subclass of skew-Brauer graph algebras, where the associated skew-Brauer graph has multiplicity function identically equal to one, generalizing a result over gentle algebras. We also characterize skew-Brauer algebras of finite representation type. Finally, we provide a geometric interpretation of cut-sets and reflections of algebras using orbifold dissections. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_01942 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Skew-Brauer graph algebras Elsener, Ana García Guazzelli, Victoria Valdivieso, Yadira Representation Theory Rings and Algebras 16G20, 05E10, 16S35, 16S70 In this work, we introduce a new class of algebras called skew-Brauer graph algebras, which generalize the well-known Brauer graph algebras. We establish that skew-Brauer graph algebras are symmetric and can be defined using a Brauer graph with additional information. We show that the class of trivial extensions of skew-gentle algebras coincides with a subclass of skew-Brauer graph algebras, where the associated skew-Brauer graph has multiplicity function identically equal to one, generalizing a result over gentle algebras. We also characterize skew-Brauer algebras of finite representation type. Finally, we provide a geometric interpretation of cut-sets and reflections of algebras using orbifold dissections. |
| title | Skew-Brauer graph algebras |
| topic | Representation Theory Rings and Algebras 16G20, 05E10, 16S35, 16S70 |
| url | https://arxiv.org/abs/2410.01942 |