# 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} }

. 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…

## References

SHOWING 1-10 OF 55 REFERENCES

### Partial (co)actions of Taft and Nichols Hopf algebras on algebras

- Mathematics
- 2022

. In this paper, we characterize suitable partial (co)actions of Taft and Nichols Hopf algebras on algebras, and moreover we get that such partial (co)actions are symmetric. For certain algebras,…

### Universal Enveloping Algebras of Lie–Rinehart Algebras as a Left Adjoint Functor

- MathematicsMediterranean Journal of Mathematics
- 2022

We prove how the universal enveloping algebra constructions for Lie–Rinehart algebras and anchored Lie algebras are naturally left adjoint functors. This provides a conceptual motivation for the…

### Partial (co)actions of Taft and Nichols Hopf algebras on their base fields

- MathematicsInt. J. Algebra Comput.
- 2021

In this paper, we determine all partial actions and partial coactions of Taft and Nichols Hopf algebras on their base fields. Furthermore, we prove that all such partial (co)actions are symmetric.

### On anchored Lie algebras and the Connes–Moscovici bialgebroid construction

- MathematicsJournal of Noncommutative Geometry
- 2022

We show how the Connes-Moscovici's bialgebroid construction naturally provides universal objects for Lie algebras acting on non-commutative algebras.

### Partial actions of a Hopf algebra on its base field and the corresponding partial smash product algebra

- MathematicsJournal of Algebra and Its Applications
- 2022

We introduce the concept of a λ-Hopf algebra as a Hopf algebra obtained as the partial smash product algebra of a Hopf algebra and its base field, and show that every Hopf algebra is a λ-Hopf…

### Algebraic structures in comodule categories over weak bialgebras

- MathematicsCommunications in Algebra
- 2022

Abstract For a bialgebra L coacting on a -algebra A, a classical result states A is a right L-comodule algebra if and only if A is an algebra in the category of right L-comodules. We generalize this…

### Dimensions

- PsychologyJournal of the Medical Library Association : JMLA
- 2019

Dimensions is a linked-research data platform that aims to reveal connections between research and its scholarly outputs.

### LIE GROUPOIDS AND LIE ALGEBROIDS IN DIFFERENTIAL GEOMETRY

- Mathematics
- 1988

4. G. D. Mostow and P. Deligne, Monodromy of hypergeometric functions and nonlattice integral monodromy, Inst. Hautes Etudes Sci. Publ. Math. 46 (1983). 5. E. Picard, Sur les fonctions hyperfuchsiaes…