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Simple ambiskew polynomial rings. (English) Zbl 1287.16024

Summary: We determine simplicity criteria in characteristics 0 and \(p\) for a ubiquitous class of iterated skew polynomial rings in two indeterminates over a base ring. One obstruction to simplicity is the possible existence of a canonical normal element \(z\). In the case where this element exists we give simplicity criteria for the rings obtained by inverting \(z\) and the rings obtained by factoring out the ideal generated by \(z\). The results are illustrated by numerous examples including higher quantized Weyl algebras and generalizations of some low-dimensional symplectic reflection algebras.

MSC:

16S36 Ordinary and skew polynomial rings and semigroup rings
16W25 Derivations, actions of Lie algebras
16D60 Simple and semisimple modules, primitive rings and ideals in associative algebras
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