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Working paper

The Arens-Michael envelope of a smash product

arxiv.org. math. Cornell University, 2011. No. 1101.0166.
Given a Hopf algebra H and an H-module algebra A, we explicitly describe the Arens-Michael envelope of the smash product A#H in terms of the Arens-Michael envelope of H and a certain completion of A. We also give an example (Manin's quantum plane) showing that the result fails for non-Hopf bialgebras.