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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

NONCOMMUTATIVE NOETHER'S PROBLEM FOR COMPLEX REFLECTION GROUPS

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Author(s):
Eshmatov, Farkhod [1] ; Futorny, Vyacheslav [2] ; Ovsienko, Sergiy [3] ; Schwarz, Joao Fernando [2]
Total Authors: 4
Affiliation:
[1] Univ Sichuan, Dept Math, Chengdu, Sichuan - Peoples R China
[2] Univ Sao Paulo, Inst Matemat & Estat, Sao Paulo - Brazil
[3] Taras Shevchenko Kiev Univ, Fac Mech & Math, Kiev - Ukraine
Total Affiliations: 3
Document type: Journal article
Source: Proceedings of the American Mathematical Society; v. 145, n. 12, p. 5043-5052, DEC 2017.
Web of Science Citations: 2
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. (AU)

FAPESP's process: 14/25612-1 - Extensions of Noether's problem and Gelfand-Kirillov's conjecture to certain classes of noncommutative algebras
Grantee:João Fernando Schwarz
Support type: Scholarships in Brazil - Doctorate
FAPESP's process: 14/09310-5 - Algebraic structures and their representations
Grantee:Vyacheslav Futorny
Support type: Research Projects - Thematic Grants
FAPESP's process: 13/22068-6 - Quantizations of Kleinian singularities and Dixmier groups
Grantee:Vyacheslav Futorny
Support type: Research Grants - Visiting Researcher Grant - International