We discuss a possible noncommutative generalization of the notion of an equivariant vector bundle. Let A be a -algebra, M a left A-module, H a Hopf -algebra, an algebra coaction, and let denote with the right A-module structure induced by delta. The usual definitions of equivariant vector bundle naturally lead, in the context of -algebras, to an -module homomorphismthat fulfills some appropriate conditions. On the other hand, sometimes an (A, H)-Hopf module is considered instead, for the same purpose. When Theta is invertible, as is always the case when H is commutative, the two descriptions are equivalent. We point out that the two notions differ in general, by giving an example of a noncommutative Hopf algebra H for which there exists such a Theta that is not invertible and a left-right (A, H)-Hopf module whose corresponding homomorphism is not an isomorphism.
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