Makoto Yamashita, University of Oslo
We relate quantum automorphism groups of finite sets to those of finite quantum sets using 2-cocycle deformation. This leads to isomorphism of the function algebras on these quantum groups up to crossed product by finite commutative group actions. Based on this, we obtain the strong 1-boundedness of von Neumann algebra for some free permutation groups, and the residually finiteness of the Hopf algebras for free orthogonal groups.
Based on joint work with Michael Brannan, Floris Elzinga, and Samuel J. Harris.