Generator Coalgebras are not Necessarily Quasi-coFrobenius |
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Authors: | Mariana Haim Blas Torrecillas |
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Institution: | (1) Department of Mathematics, University of Kentucky, Lexington, Ky, 40506, U.S.A.;(2) Departamento de Álgebra y Análisis Matemático, Universidad De Almería, 04120 Almería, Spain |
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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 Nastasescu et al. (Algebr Represent Theory 11(2):179–190, 2008). We also prove it is true for monomial pointed coalgebras and we characterize the quivers Q such that
\mathbbkQ\mathbb{k}Q admits a monomial subcoalgebra that is left (right) quasi-coFrobenius. |
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