On Dual Algebras of Hopf Algebroids

TL;DR

This paper explores the dual algebra structures of Hopf algebroids, providing insights into their comodules by relating them to modules over the dual algebra, thus advancing the understanding of their algebraic properties.

Contribution

It offers a new perspective on the duality of Hopf algebroids and characterizes comodules as modules over the dual algebra, enriching the theoretical framework.

Findings

Comodules over a Hopf algebroid can be viewed as modules over its dual algebra.

Provides a detailed understanding of the dual algebra structure of Hopf algebroids.

Establishes a correspondence between comodules and modules in this context.

Abstract

We study the dual algebras of (discrete) Hopf algebroids. In particular, we understand comodules over a Hopf algebroid as (discrete) modules over its dual algebra.