• Corpus ID: 252531547

Cocommutative Hopf-like actions on algebras

@inproceedings{Calderon2022CocommutativeHA,
  title={Cocommutative Hopf-like actions on algebras},
  author={Fabio Calder'on and Hongdi Huang and Elizabeth Wicks and Robert J. Won},
  year={2022}
}

• F. Calder'on, Hongdi Huang, +1 author R. Won
• Published 24 September 2022
• Mathematics

. We call an algebraic structure H “Hopf-like” if its category of (co)represen-tations is monoidal. Here, we study algebras A in such monoidal categories when H is cocommutative, including when H is a cocommutative Hopf algebra, is a groupoid (algebra), and is, more generally, a cocommutative weak Hopf algebra. We establish that A is an H -module algebra precisely when there exists a structure preserving map from H to a certain collection of linear endomorphisms of A that has the same structure as H . This yields an equivalence between categorical and representation-theoretic notions of an algebra A admitting an action of H . Many examples are included throughout.