Deformations of Euclidean supersymmetries

We consider quantum supergroups that arise in nonanticommutative deformations of the N=(1/2, 1/2) and N=(1, 1) four-dimensional Euclidean supersymmetric theories. Twist operators in the corresponding superspaces and deformed superfield algebras contain left spinor generators. We show that nonanticommutative *-products of superfields transform covariantly under the deformed supersymmetries. This covariance guarantees the invariance of the deformed superfield actions of models involving *-products of superfields. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 147, No. 2, pp. 270–289, May, 2006.