Kenny De Commer: Spectral *-algebras and quantum group actions

Abstract: Given a *-algebra A, one can consider its representations on Hilbert spaces satisfying certain prescribed spectral conditions. We consider how in certain cases one can construct from this a universal C*-algebra. We then consider how the spectral conditions need to be modified if one wants to incorporate on the C*-algebra also the action of a compact quantum group on the *-algebra A. If there is time, we explain how this can be applied to determine the operator algebra structure of quantum symmetric spaces.