The structure theorems for Yetter-Drinfeld comodule algebras

In this paper, we first introduce the notion of a Yetter-Drinfeld comodule algebra and give examples. Then we give the structure theorems of Yetter-Drinfeld comodule algebras. That is, if $L$ is a Yetter-Drinfeld Hopf algebra and $A$ is a right $L$-Yetter-Drinfeld comodule algebra, then there exists an algebra isomorphism between $A$ and $A^{coL} \mathbin{\sharp} H$, where $A^{coL}$ is the coinvariant subalgebra of $A$.