Generator coalgebras are not necessarily quasi-coFrobenius

Details Generator coalgebras are not necessarily quasi-coFrobenius Generator coalgebras are not necessarily quasi-coFrobenius

2008-09-25

arxiv.org/abs/0809.4410v2

Mathematics

Rings and Algebras

Scientific paper

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 $Q$ such that $\Bbbk Q$ admits a monomial subcoalgebra that is left (right) quasi-coFrobenius.

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