Algebraic quantum permutation groups

By Julien Bichon. 2007

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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 $K^n$: 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 $K^n$, on which we determine the possible group gradings when $K$ is algebraically closed and has characteristic zero.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/97f4412d4fc4fd7925261db8052227ef6a8f1381