• DOI:10.1080/00927872.2019.1631320
• Corpus ID: 119309207

On noncommutative equivariant bundles

@article{DAndrea2016OnNE,
  title={On noncommutative equivariant bundles},
  author={Francesco D’Andrea and Alessandro De Paris},
  journal={Communications in Algebra},
  year={2016},
  volume={47},
  pages={5443 - 5461}
}

• F. D’Andrea, Alessandro De Paris
• Published 9 June 2016
• Mathematics
• Communications in Algebra

Abstract 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 δ. 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 Θ 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 Θ that is not invertible and a left-right (A, H)-Hopf module whose corresponding homomorphism is not an isomorphism.