English

Generator coalgebras are not necessarily quasi-coFrobenius

Rings and Algebras 2009-03-17 v2 Quantum Algebra

Abstract

We study the problem of whether a coalgebra that generates its category of left (right) comodules is left (right) quasi-coFrobenius or not. We prove it does not hold in general, by giving a method of constructing counterexamples. This gives a negative answer to a question stated in \cite{kn:coalgen}. We also prove it is true for monomial pointed coalgebras and we characterize the quivers QQ such that kQ\Bbbk Q admits a monomial subcoalgebra that is left (right) quasi-coFrobenius.

Keywords

Cite

@article{arxiv.0809.4410,
  title  = {Generator coalgebras are not necessarily quasi-coFrobenius},
  author = {Mariana Haim and Blas Torrecillas},
  journal= {arXiv preprint arXiv:0809.4410},
  year   = {2009}
}