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arXiv · 2501.13476

Maximal finite semibricks consist only of open bricks

Sota Asai
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Abstract

A semibrick is a set of modules satisfying Schur's Lemma, and it is said to be maximal if it is not properly contained in another semibrick. For any finite dimensional algebra $\varLambda$ over an algebracally closed field $K$, we prove that any maximal finite semibrick $\mathcal{S}$ consists only of open bricks $B$, that is, bricks whose orbit closures $\overline{\mathcal{O}_B}$ are irreducible components in the representation schemes.

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Sota Asai. 2025-01-23. Maximal finite semibricks consist only of open bricks. https://arxiv.org/abs/2501.13476

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