Twisted bialgebroids versus bialgebroids from a Drinfeld twist

@article{Borowiec2016TwistedBV,
  title={Twisted bialgebroids versus bialgebroids from a Drinfeld twist},
  author={Andrzej Borowiec and Anna Pachoł},
  journal={arXiv: Mathematical Physics},
  year={2016}
}
Bialgebroids (resp. Hopf algebroids) are bialgebras (Hopf algebras) over noncommutative rings. Drinfeld twist techniques are particularly useful in the (deformation) quantization of Lie algebras as well as underlying module algebras (=quantum spaces). Smash product construction combines these two into the new algebra which, in fact, does not depend on the twist. However, we can turn it into bialgebroid in the twist dependent way. Alternatively, one can use Drinfeld twist techniques in a… 
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