Universal deformation rings of a special class of modules over generalized Brauer tree algebras
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| author | Caranguay-Mainguez, Jhony F. Rizzo, Pedro Vélez-Marulanda, José A. |
| author_facet | Caranguay-Mainguez, Jhony F. Rizzo, Pedro Vélez-Marulanda, José A. |
| contents | Let $\Bbbk$ be an algebraically closed field and $Λ$ a generalized Brauer tree algebra over $\Bbbk$. We compute the universal deformation rings of the periodic string modules over $Λ$. Moreover, for a specific class of generalized Brauer tree algebras $Λ(n,\overline{m})$, we classify the universal deformation rings of the modules lying in $Ω$-stable components $\mathfrak{C}$ of the stable Auslander-Reiten quiver provided that $\mathfrak{C}$ contains at least one simple module. Our approach uses several tools and techniques from the representation theory of Brauer graph algebras. Notably, we leverage Duffield's work on the Auslander-Reiten theory of these algebras and Opper-Zvonareva's results on derived equivalences between Brauer graph algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_09678 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Universal deformation rings of a special class of modules over generalized Brauer tree algebras Caranguay-Mainguez, Jhony F. Rizzo, Pedro Vélez-Marulanda, José A. Representation Theory Rings and Algebras 16G10 (Primary) 16G20, 16G70 (Secondary) Let $\Bbbk$ be an algebraically closed field and $Λ$ a generalized Brauer tree algebra over $\Bbbk$. We compute the universal deformation rings of the periodic string modules over $Λ$. Moreover, for a specific class of generalized Brauer tree algebras $Λ(n,\overline{m})$, we classify the universal deformation rings of the modules lying in $Ω$-stable components $\mathfrak{C}$ of the stable Auslander-Reiten quiver provided that $\mathfrak{C}$ contains at least one simple module. Our approach uses several tools and techniques from the representation theory of Brauer graph algebras. Notably, we leverage Duffield's work on the Auslander-Reiten theory of these algebras and Opper-Zvonareva's results on derived equivalences between Brauer graph algebras. |
| title | Universal deformation rings of a special class of modules over generalized Brauer tree algebras |
| topic | Representation Theory Rings and Algebras 16G10 (Primary) 16G20, 16G70 (Secondary) |
| url | https://arxiv.org/abs/2504.09678 |