Noncommutative Noether’s problem for complex reflection groups
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- by Farkhod Eshmatov, Vyacheslav Futorny, Sergiy Ovsienko and Joao Fernando Schwarz PDF
- Proc. Amer. Math. Soc. 145 (2017), 5043-5052 Request permission
Abstract:
We solve some noncommutative analogue of the Noether’s problem for the reflection groups by showing that the skew field of fractions of the invariant subalgebra of the Weyl algebra under the action of any finite complex reflection group is a Weyl field, that is, isomorphic to the skew field of fractions of some Weyl algebra. We also extend this result to the invariants of the ring of differential operators on any finite dimensional torus. The results are applied to obtain analogs of the Gelfand-Kirillov conjecture for Cherednik algebras and Galois algebras.References
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Additional Information
- Farkhod Eshmatov
- Affiliation: Department of Mathematics, University of Sichuan, Chengdu, People’s Republic of China
- Email: olimjon55@hotmail.com
- Vyacheslav Futorny
- Affiliation: Instituto de Matemática e Estatística, Universidade de São Paulo, São Paulo, Brazil
- MR Author ID: 238132
- Email: futorny@ime.usp.br
- Sergiy Ovsienko
- Affiliation: Faculty of Mechanics and Mathematics, Taras Shevchenko Kiev University Kiev, Ukraine
- Email: ovsiyenko.sergiy@gmail.com
- Joao Fernando Schwarz
- Affiliation: Instituto de Matemática e Estatística, Universidade de São Paulo, São Paulo, Brazil
- MR Author ID: 1130675
- Email: jfschwarz.0791@gmail.com
- Received by editor(s): July 3, 2015
- Received by editor(s) in revised form: November 27, 2016
- Published electronically: August 29, 2017
- Additional Notes: The first author was supported in part by Fapesp (2013/22068-6)
The second author was supported in part by CNPq (301320/2013-6) and by Fapesp (2014/09310-5)
The fourth author was supported in part by Fapesp (2014/25612-1) - Communicated by: Harm Derksen
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 5043-5052
- MSC (2010): Primary 16Z05, 16R30
- DOI: https://doi.org/10.1090/proc/13646
- MathSciNet review: 3717935