Representation embeddings and the second Brauer-Thrall conjecture
Representation Theory
2023-05-30 v5
Abstract
We prove that over an algebraically closed field there is a representation embedding from the category of classical Kronecker-modules without the simple injective into the category of finite-dimensional modules over any representation-infinite finite-dimensional algebra. We also sharpen some known results on representation embeddings, we simplify some proofs and we construct a simultaneous orthogonal embedding for an infinite family of module categories. In the last section the minimal classes of representation-infinite algebras are determined. The result depends on the characteristic.
Cite
@article{arxiv.1611.02017,
title = {Representation embeddings and the second Brauer-Thrall conjecture},
author = {Klaus Bongartz},
journal= {arXiv preprint arXiv:1611.02017},
year = {2023}
}