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ЖУРНАЛЫ // Algebra and Discrete Mathematics // Архив

Algebra Discrete Math., 2017, том 23, выпуск 1, страницы 35–46 (Mi adm595)

Эта публикация цитируется в 3 статьях

SURVEY ARTICLE

Galois orders of symmetric differential operators

Vyacheslav Futorny, João Schwarz

Instituto de Matemática e Estatística, Universidade de São Paulo, São Paulo SP, Brasil

Аннотация: 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 Weyl 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 quantum case for $\mathrm{gl}_n$ and $\mathrm{sl}_n$ 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.

Ключевые слова: Weyl algebra, invariant differential operators, Galois order, filed of fractions.

MSC: 13N10, 16D30, 16S32, 16S85

Поступила в редакцию: 21.03.2017

Язык публикации: английский



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