Abstract
For a finite-index [Formula: see text] subfactor [Formula: see text], we prove the existence of a universal Hopf ∗-algebra (or, a discrete quantum group in the analytic language) acting on [Formula: see text] in a trace-preserving fashion and fixing [Formula: see text] pointwise. We call this Hopf ∗-algebra the quantum Galois group for the subfactor and compute it in some examples of interest, notably for arbitrary irreducible finite-index depth-two subfactors. Along the way, we prove the existence of universal acting Hopf algebras for more general structures (tensors in enriched categories), in the spirit of recent work by Agore, Gordienko and Vercruysse.
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