Algebraic Quantum Permutation Groups
نویسنده
چکیده
We discuss some algebraic aspects of quantum permutation groups, working over arbitrary fields. If K is any characteristic zero field, we show that there exists a universal cosemisimple Hopf algebra coacting on the diagonal algebra K: this is a refinement of Wang’s universality theorem for the (compact) quantum permutation group. We also prove a structural result for Hopf algebras having a non-ergodic coaction on the diagonal algebra K, on which we determine the possible group gradings when K is algebraically closed and has characteristic zero.
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