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On generic bricks over tame algebras

Published 28 Aug 2024 in math.RT | (2408.16127v1)

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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