Abstract
In this article we give a description for the centralizer of the coefficient ring R in the skew PBW extension \(\sigma (R) \). We give an explicit description in the quasi-commutative case and state a necessary condition in the general case. We also consider the PBW extension \(\sigma (\mathcal {A}) \) of the algebra of functions with finite support on a countable set, describing the centralizer of \(\mathcal {A}\) and the center of the skew PBW extension.
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