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arXiv · 2408.16127

On generic bricks over tame algebras

R. Bautista·E. Pérez·L. Salmerón
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Abstract

We prove that if ${\Lambda}$ is a tame finite-dimensional algebra over an algebraically closed field and $G$ is a generic ${\Lambda}-$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 ${\Lambda}$ admits a generic brick if and only if ${\Lambda}$ is brick-continuous.

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R. Bautista, E. Pérez, L. Salmerón. 2024-08-28. On generic bricks over tame algebras. https://arxiv.org/abs/2408.16127

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