English

A counterexample to a conjecture on Cartan determinants of monoid algebras

Representation Theory 2023-06-27 v1 Rings and Algebras

Abstract

We show that there are finite monoids MM such that the Cartan matrix of the monoid algebra CM\mathbb C M is non-singular, whilst the Cartan matrix of kMkM is singular for some field kk of positive characteristic, disproving a recent conjecture of Steinberg.

Keywords

Cite

@article{arxiv.2306.14002,
  title  = {A counterexample to a conjecture on Cartan determinants of monoid algebras},
  author = {Florian Eisele},
  journal= {arXiv preprint arXiv:2306.14002},
  year   = {2023}
}