On generic bricks over tame algebras
Fuente:
arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914470212665344 |
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| author | Bautista, R. Pérez, E. Salmerón, L. |
| author_facet | Bautista, R. Pérez, E. Salmerón, L. |
| contents | We prove that if $Λ$ is a tame finite-dimensional algebra over an algebraically closed field and $G$ is a generic $Λ-$module, then $G$ is a generic brick if and only if it determines a one-parameter family of bricks with the same dimension. In particular, we obtain that $Λ$ admits a generic brick if and only if $Λ$ is brick-continuous. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_16127 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On generic bricks over tame algebras Bautista, R. Pérez, E. Salmerón, L. Representation Theory 16E45, 16E30, 16W50, 18E30, 18E10 We prove that if $Λ$ is a tame finite-dimensional algebra over an algebraically closed field and $G$ is a generic $Λ-$module, then $G$ is a generic brick if and only if it determines a one-parameter family of bricks with the same dimension. In particular, we obtain that $Λ$ admits a generic brick if and only if $Λ$ is brick-continuous. |
| title | On generic bricks over tame algebras |
| topic | Representation Theory 16E45, 16E30, 16W50, 18E30, 18E10 |
| url | https://arxiv.org/abs/2408.16127 |