Portal de Periódicos da CAPES

Symmetric coalgebras

2004; Elsevier BV; Volume: 279; Issue: 1 Linguagem: Inglês

10.1016/j.jalgebra.2004.05.007

1090-266X

Florencio Castaño Iglesias, S. Dăscălescu, C. Năstăsescu,

Homotopy and Cohomology in Algebraic Topology

We construct a structure of a ring with local units on a co-Frobenius coalgebra. We study a special class of co-Frobenius coalgebras whose objects we call symmetric coalgebras. We prove that any semiperfect coalgebra can be embedded in a symmetric coalgebra. We use a dual version of Brauer's equivalence theorem to characterize symmetric coalgebras by comparing certain functors. We define an automorphism of the ring with local units constructed from a co-Frobenius coalgebra, which we call the Nakayama automorphism. This is used to give a new characterization to symmetric coalgebras and to describe Hopf algebras that are symmetric as coalgebras. As a corollary we obtain as a consequence the known characterization of Hopf algebras that are symmetric as algebras.