Galois coverings of pointed coalgebras

TL;DR

This paper introduces Galois coverings for pointed coalgebras, showing they can be represented via smash coproducts and are equivalent to group gradings, without finiteness constraints.

Contribution

It develops a new theory connecting Galois coverings of pointed coalgebras with smash coproducts and group gradings, expanding the understanding of coalgebra symmetries.

Findings

Galois coverings are expressed by smash coproducts via automorphism group coactions.

The theory establishes an equivalence between Galois coverings and group gradings.

No finiteness assumptions are needed for the grading group or quiver.

Abstract

We introduce the concept of a Galois covering of a pointed coalgebra. The theory developed shows that Galois coverings of pointed coalgebras can be concretely expressed by smash coproducts using the coaction of the automorphism group of the covering. Thus the theory of Galois coverings is seen to be equivalent to group gradings of coalgebras. An advantageous feature of the coalgebra theory is that neither the grading group nor the quiver is assumed finite in order to obtain a smash product coalgebra.