Cofrobenius Coalgebra

Details Cofrobenius Coalgebra Cofrobenius Coalgebra

2006-04-11

arxiv.org/abs/math/0604251v1

Mathematics

Quantum Algebra

9 pages, to appear in J. Algebra

Scientific paper

We investigate left and right co-Frobenius coalgebras and give equivalent characterizations which prove statements dual to the characterizations of Frobenius algebras. We prove that a coalgebra is left and right co-Frobenius if and only if C is isomorphic to Rat(C*) as right C*-modules and also that this is eqhivalent to the fact that the functors Hom_K(-,K) and Hom_{C*}(-,C*) from the category of right C-comodules to the category of all left C*-modules are isomorphic. This allows a definition of a left-right symmetric concept of co-Frobenius coalgebras that is perfectly dual to the one of Frobenius algebras and coincides to the existing notion left and right co-Frobenius coalgebra.

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