On generic bricks over tame algebras

Abstract

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