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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.)

Galois orders of symmetric differential operators

Author(s):
Futorny, Vyacheslav ; Schwarz, Joao
Total Authors: 2
Document type: Journal article
Source: ALGEBRA & DISCRETE MATHEMATICS; v. 23, n. 1, p. 35-46, 2017.
Web of Science Citations: 0
Abstract

In this survey we discuss the theory of Galois rings and orders developed in ({[}20], {[}22]) by Sergey Ovsienko and the first author. This concept allows to unify the representation theories of Generalized Wey1 Algebras ({[}4]) and of the universal enveloping algebras of Lie algebras. It also had an impact on the structure theory of algebras. In particular, this abstract framework has provided a new proof of the Gelfand-Kirillov Conjecture ({[}24]) in the classical and the quarittini case for gl(n), and sl(n) in {[}18] and {[}21], respectively. We will give a detailed proof of the Gelfand-Kirillov Conjecture in the classical case and show that the algebra of symmetric differential operators has a structure of a Galois order. (AU)

FAPESP's process: 14/09310-5 - Algebraic structures and their representations
Grantee:Vyacheslav Futorny
Support type: Research Projects - Thematic Grants
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