English

Maximal finite semibricks consist only of open bricks

Representation Theory 2025-09-16 v3

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 Λ\varLambda over an algebracally closed field KK, we prove that any maximal finite semibrick S\mathcal{S} consists only of open bricks BB, that is, bricks whose orbit closures OB\overline{\mathcal{O}_B} are irreducible components in the representation schemes.

Keywords

Cite

@article{arxiv.2501.13476,
  title  = {Maximal finite semibricks consist only of open bricks},
  author = {Sota Asai},
  journal= {arXiv preprint arXiv:2501.13476},
  year   = {2025}
}

Comments

9 pages, comments welcome