Multiplier Hopf Algebras in Categories and the Biproduct Construction |
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Authors: | L. Delvaux |
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Affiliation: | (1) Department of Mathematics, UHasselt, Agoralaan, 3590 Diepenbeek, Belgium |
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Abstract: | Let B be a regular multiplier Hopf algebra. Let A be an algebra with a non-degenerate multiplication such that A is a left B-module algebra and a left B-comodule algebra. By the use of the left action and the left coaction of B on A, we determine when a comultiplication on A makes A into a “B-admissible regular multiplier Hopf algebra.” If A is a B-admissible regular multiplier Hopf algebra, we prove that the smash product A # B is again a regular multiplier Hopf algebra. The comultiplication on A # B is a cotwisting (induced by the left coaction of B on A) of the given comultiplications on A and B. When we restrict to the framework of ordinary Hopf algebra theory, we recover Majid’s braided interpretation of Radford’s biproduct. Presented by K. Goodearl. |
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Keywords: | Multiplier Hopf algebra Biproduct construction Radford’ s biproduct Category |
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