Maximal finite semibricks consist only of open bricks
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915493070241792 |
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| author | Asai, Sota |
| author_facet | Asai, Sota |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_13476 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Maximal finite semibricks consist only of open bricks Asai, Sota Representation Theory 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. |
| title | Maximal finite semibricks consist only of open bricks |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2501.13476 |