Deformations of Euclidean Supersymmetries

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We consider quantum supergroups that arise in non-anticommutative deformations of N=(1/2,1/2) and N=(1,1) four-dimensional Euclidean supersymmetric theories. Twist operators in the corresponding deformed algebras of superfields contain left spinor generators. We show that non-anticommutative ⋆-products of superfields transform covariantly in the deformed supersymmetries. This covariance guarantees the invariance of deformed superfield actions of models involving ⋆-products of superfields.