Abstract
In this article we give a description for the centralizer of the coefficient ring R in the skew PBW extension \(\sigma (R)<x_1,x_2,\ldots ,x_n>\). 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 \(\sigma (\mathcal {A})<x_1,x_2,\ldots ,x_n>\) 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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Acknowledgements
This research was supported by the Swedish International Development Cooperation Agency (Sida) and International Science Programme (ISP) in Mathematical Sciences (IPMS), Eastern Africa Universities Mathematics Programme (EAUMP). Alex Behakanira Tumwesigye is also grateful to the research environment Mathematics and Applied Mathematics (MAM), Division of Applied Mathematics, Mälardalen University for providing an excellent and inspiring environment for research education and research.
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Tumwesigye, A.B., Richter, J., Silvestrov, S. (2020). Centralizers in PBW Extensions. In: Silvestrov, S., Malyarenko, A., Rančić, M. (eds) Algebraic Structures and Applications. SPAS 2017. Springer Proceedings in Mathematics & Statistics, vol 317. Springer, Cham. https://doi.org/10.1007/978-3-030-41850-2_20
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DOI: https://doi.org/10.1007/978-3-030-41850-2_20
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