English

On generic bricks over tame algebras

Representation Theory 2026-04-15 v2

Abstract

We prove that if Λ{\Lambda} is a tame finite-dimensional algebra over an algebraically closed field and GG is a generic Λ{\Lambda}-module, then GG is a generic brick if and only if it determines a one-parameter family of bricks with the same dimension. In particular, we obtain that Λ{\Lambda} admits a generic brick if and only if Λ{\Lambda} is brick-continuous.

Keywords

Cite

@article{arxiv.2408.16127,
  title  = {On generic bricks over tame algebras},
  author = {R. Bautista and E. Pérez and L. Salmerón},
  journal= {arXiv preprint arXiv:2408.16127},
  year   = {2026}
}
R2 v1 2026-06-28T18:27:04.842Z