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arXiv · 2608.00395

On bricks of one-point extension algebras

Qi Wang
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Abstract

Let $\Lambda=B[E]$ be the one-point extension algebra of $B$ by the extension module $E$. Using the standard triple description of $\Lambda$-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 $\Lambda$.

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Qi Wang. 2026-08-01. On bricks of one-point extension algebras. https://arxiv.org/abs/2608.00395

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