On bricks of one-point extension algebras

Abstract

Let $Λ=B[E]$ be the one-point extension algebra of $B$ by the extension module $E$. Using the standard triple description of $Λ$-modules, we characterize mixed bricks through an injectivity condition and a scalar-stabilizer condition. Under the assumption that $B$ is $E$-visible finite, we interpret mixed bricks as orbits in Grassmannians and derive a necessary and sufficient criterion for the brick-finiteness of $Λ$.