  In this work, we study another characterization of Yetter-Drinfeld algebras
over finite-dimensional Hopf algebras. We show the equivalence between this
characterization, called the "only coaction" characterization, and the standard
"action-coaction" characterization. This modern approach for Yetter-Drinfeld
algebras is one of the key ingredient in a self-dual theory of quantum
transformation groupoids arising from actions of quantum groups.
