| Full text | |
| Author(s): |
Total Authors: 2
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| Affiliation: | [1] Univ Sao Paulo, Inst Matemat & Estat, Sao Paulo, SP - Brazil
Total Affiliations: 1
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| Document type: | Journal article |
| Source: | Journal of Algebra; v. 542, p. 215-229, JAN 15 2020. |
| Web of Science Citations: | 0 |
| Abstract | |
We prove that an invariant subalgebra A(n)(W)of the Weyl algebra A(n) is a Galois order over an adequate commutative subalgebra Gamma when W is a two-parameters irreducible unitary reflection group G(m, 1, n), m >= 1, n >= 1, including the Weyl group of type B-n, or alternating group A(n), or the product of n copies of a cyclic group of fixed finite order. Earlier this was established for the symmetric group in {[}15]. In each of the cases above, except for the alternating groups, we show that A(n)(W) is free as a right (left) Gamma-module. Similar results are established for the algebra of W-invariant differential operators on the n-dimensional torus where W is a symmetric group S-n or orthogonal group of type B-n or D-n. As an application of our technique we prove the quantum Gelfand-Kirillov conjecture for U-q(sl(2)), the first Witten deformation and the Woronowicz deformation. (C) 2019 Elsevier Inc. All rights reserved. (AU) | |
| FAPESP's process: | 18/18146-5 - Ore Domainas: localizations, invariants and representations. |
| Grantee: | João Fernando Schwarz |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |
| FAPESP's process: | 16/14648-0 - Geometric methods in representation theory |
| Grantee: | João Fernando Schwarz |
| Support Opportunities: | Scholarships abroad - Research Internship - Doctorate |
| 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 Opportunities: | Scholarships in Brazil - Doctorate |
| FAPESP's process: | 18/23690-6 - Structures, representations, and applications of algebraic systems |
| Grantee: | Ivan Chestakov |
| Support Opportunities: | Research Projects - Thematic Grants |