Abstract
We begin by reviewing a classical result on the algebraic dependence of commuting elements in the Weyl algebra. We proceed by describing generalizations of this result to various classes of Ore extensions, including both results that are already known and one new result.
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Acknowledgments
The author wishes to thank Fredrik Ekström, Johan Öinert and Sergei Silvestrov for helpful comments. The author is also grateful to the Dalhgren and Lanner foundations for support. This research was also supported in part by the Swedish Foundation for International Cooperation in Research and Higher Education (STINT), The Swedish Research Council (grant no. 2007-6338), The Royal Swedish Academy of Sciences, The Crafoord Foundation and the NordForsk Research Network “Operator Algebras and Dynamics” (grant no. 11580).
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Richter, J. (2014). Burchnall-Chaundy Theory for Ore Extensions. In: Makhlouf, A., Paal, E., Silvestrov, S., Stolin, A. (eds) Algebra, Geometry and Mathematical Physics. Springer Proceedings in Mathematics & Statistics, vol 85. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55361-5_4
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DOI: https://doi.org/10.1007/978-3-642-55361-5_4
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