caa a22 4500 60616068X CHVBK 20210128100631.0 cr unu---uuuuu 210128e20151201xx s 000 0 eng 10.1007/s10468-015-9553-8 doi (NATIONALLICENCE)springer-10.1007/s10468-015-9553-8 Noetherian Algebras of Quantum Differential Operators [Elektronische Daten] [Uma Iyer, David Jordan] We consider algebras of quantum differential operators, for appropriate bicharacters on a polynomial algebra in one indeterminate and for the coordinate algebra of quantum n-space for n ≥ 3. In the former case a set of generators for the quantum differential operators was identified in work by the first author and T. C. McCune but it was not known whether the algebra is Noetherian. We answer this question affirmatively, setting it in a more general context involving the behaviour Noetherian condition under localization at the powers of a single element. In the latter case we determine the algebra of quantum differential operators as a skew group algebra of the group Z n $\mathbb {Z}^{n}$ over a quantized Weyl algebra. It follows from this description that this algebra is a simple right and left Noetherian domain. Springer Science+Business Media Dordrecht, 2015 Noetherian rings nationallicence Quantum differential operators nationallicence Iyer Uma Department of Mathematics and Computer Science, Bronx Community College, 2155 University Avenue, 10453, Bronx, New York, USA aut Jordan David School of Mathematics and Statistics, University of Sheffield, Hicks Building, S3 7RH, Sheffield, UK aut Algebras and Representation Theory Springer Netherlands 18/6(2015-12-01), 1593-1622 1386-923X 18:6<1593 2015 18 10468 https://doi.org/10.1007/s10468-015-9553-8 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10468-015-9553-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Iyer Uma Department of Mathematics and Computer Science, Bronx Community College, 2155 University Avenue, 10453, Bronx, New York, USA aut NATIONALLICENCE 700 1- Jordan David School of Mathematics and Statistics, University of Sheffield, Hicks Building, S3 7RH, Sheffield, UK aut NATIONALLICENCE 773 0- Algebras and Representation Theory Springer Netherlands 18/6(2015-12-01), 1593-1622 1386-923X 18:6<1593 2015 18 10468