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Fréchet Quantum Supergroups

In this paper, we introduce Fréchet quantum supergroups and their representations. By using the universal deformation formula of the abelian supergroups R^{m|n} we construct various classes of Fréchet quantum supergroups that are deformation of classical ones. For such quantum supergroups, we find an analog of Kac-Takesaki operators that are superunitary and satisfy the pentagonal relation.