中文

Symmetric coalgebras

量子代数 2016-08-16 v1

摘要

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. A dual version of Brauer's equivalence theorem is presented, allowing a characterization of 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.

关键词

引用

@article{arxiv.math/0311003,
  title  = {Symmetric coalgebras},
  author = {F. Castaño Iglesias and S. Dascalescu and C. Nastasescu},
  journal= {arXiv preprint arXiv:math/0311003},
  year   = {2016}
}

备注

23 pages