2006/04/11 by Miodrag-Cristian Iovanov, Iovanov, Miodrag-Cristian
Mathematics · #16W30 #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.QA #math.RA #math.RT #msc:16W30
paper · pdf · doi:10.48550/arxiv.math/0604251
9 pages, to appear in J. Algebra
arxiv created 2006/04/11 · arxiv updated 2009/12/01
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 HomK(-,K) and HomC*(-,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.