The Arens-Michael envelope of a smash product

2010/12/30 by A. Yu. Pirkovskii, Pirkovskii, A. Yu.
Mathematics · #16S40 #46H05 #FOS: Mathematics #Functional Analysis (math.FA) #Rings and Algebras (math.RA) #math.FA #math.RA #msc:16S40 #msc:46H05

paper · pdf · doi:10.48550/arxiv.1101.0166

6 pages

arxiv created 2010/12/30 · arxiv updated 2011/01/04

Abstract

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.

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