Hopf modules, Frobenius functors and (one-sided) Hopf algebras

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:225

Article

Saracco, Paolo¹ 

[1] Univ Libre Bruxelles, Dept Mathemat, Blvd Triomphe, B-1050 Brussels, Belgium

关键词: Frobenius functors;    One-sided Hopf algebras;    Hopf modules;    Frobenius algebras;    FH-algebras;    Adjoint triples;   

DOI  :  10.1016/j.jpaa.2020.106537

来源: Elsevier

【 摘 要 】

We investigate the property of being Frobenius for some functors strictly related with Hopf modules over a bialgebra and how this property reflects on the latter. In particular, we characterize one-sided Hopf algebras with anti-(co)multiplicative one-sided antipode as those for which the free Hopf module functor is Frobenius. As a by-product, this leads us to relate the property of being an FH-algebra (in the sense of Pareigis) for a given bialgebra with the property of being Frobenius for certain naturally associated functors. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free