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We discuss a general construction of a deformation of a smash product algebracoming from an action of a particular Hopf algebra. This Hopf algebra isgenerated by skew-primitive and group-like elements, and depends on a complexparameter. The smash product algebra is defined on the quantum symmetricalgebra of a finite-dimensional vector space and a group. In particular, anapplication of this result has enabled us to find a deformation of such a smashproduct algebra which is, to the best of our knowledge, the first known exampleof a deformation in which the new relations in the deformed algebra involveelements of the original vector space. Using Hochschild cohomology, we showthat the resulting deformations are nontrivial by giving the precisecharacterization of the infinitesimal.

Deformations of Quantum Symmetric Algebras Extended by Groups