| Autor(es): |
Futorny, Vyacheslav
;
Schwarz, Joao
Número total de Autores: 2
|
| Tipo de documento: | Artigo Científico |
| Fonte: | ALGEBRA & DISCRETE MATHEMATICS; v. 23, n. 1, p. 35-46, 2017. |
| Citações Web of Science: | 0 |
| Resumo | |
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) | |
| Processo FAPESP: | 14/09310-5 - Estruturas algébricas e suas representações |
| Beneficiário: | Vyacheslav Futorny |
| Modalidade de apoio: | Auxílio à Pesquisa - Temático |
| Processo FAPESP: | 14/25612-1 - Extensões do problema de Noether e conjectura de Gelfand-Kirillov para certas classes de álgebras não-comutativas |
| Beneficiário: | João Fernando Schwarz |
| Modalidade de apoio: | Bolsas no Brasil - Doutorado |