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- W156787181 abstract "Dixmier discovered that the centralizers of elements of the first Weyl algebra have some unexpected properties. Sometimes a centralizer is not integrally closed. Also there are cases when the field of fractions of a centralizer is not a purely transcendental field. In this article I am going to discuss what happens if the Weyl algebra is replaced by the quantum plane algebra or a quantum space algebra of any dimension. I became interested in this question after a conversation with L. Small and J. Zhang during a meeting in Taiwan in June of 2001. To my great surprise it turns out that though the centralizers (of non-central elements) are not necessarily integrally closed, the fields of fractions of centralizers of non-constants are always purely transcendental fields of dimension 1 for a “general position” situation." @default.
- W156787181 created "2016-06-24" @default.
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- W156787181 date "2006-07-26" @default.
- W156787181 modified "2023-09-26" @default.
- W156787181 title "Centralizers in the quantum plane algebra" @default.
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- W156787181 doi "https://doi.org/10.1007/0-8176-4478-4_16" @default.
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