A study of Galois objects for algebraic quantum groups

Details A study of Galois objects for algebraic quantum groups A study of Galois objects for algebraic quantum groups

2007-11-08

arxiv.org/abs/0711.1319v1

Journal of Algebra 321 (6) (2009), 1746-1785

Mathematics

Quantum Algebra

32 pages

Scientific paper

We supplement the study of Galois theory for algebraic quantum groups started in the paper 'Galois Theory for Multiplier Hopf Algebras with Integrals' by A. Van Daele and Y.H. Zhang. We examine the structure of the Galois objects: algebras equipped with a Galois coaction such that only the scalars are coinvariants. We show how their structure is as rich as the one of the quantum groups themselves: there are two distinguished weak K.M.S. functionals, related by a modular element, and there is an analogue of the antipode squared. We also show how to reflect the quantum group across the Galois object to obtain a (possibly) new algebraic quantum group. We end by considering an example.

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