Galois orders of symmetric differential operators
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 impa...
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| Дата: | 2017 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2017
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/442 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543306691903488 |
|---|---|
| author | Futorny, Vyacheslav Schwarz, João |
| author_facet | Futorny, Vyacheslav Schwarz, João |
| author_sort | Futorny, Vyacheslav |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2017-04-10T07:40:45Z |
| description | 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 \(gl_n\) 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. |
| first_indexed | 2025-12-02T15:26:44Z |
| format | Article |
| id | admjournalluguniveduua-article-442 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:26:44Z |
| publishDate | 2017 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-4422017-04-10T07:40:45Z Galois orders of symmetric differential operators Futorny, Vyacheslav Schwarz, João Weyl algebra, invariant differential operators, Galois order, filed of fractions 13N10, 16D30, 16S32, 16S85 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 \(gl_n\) 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. Lugansk National Taras Shevchenko University 2017-04-10 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/442 Algebra and Discrete Mathematics; Vol 23, No 1 (2017) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/442/92 Copyright (c) 2017 Algebra and Discrete Mathematics |
| spellingShingle | Weyl algebra invariant differential operators Galois order filed of fractions 13N10 16D30 16S32 16S85 Futorny, Vyacheslav Schwarz, João Galois orders of symmetric differential operators |
| title | Galois orders of symmetric differential operators |
| title_full | Galois orders of symmetric differential operators |
| title_fullStr | Galois orders of symmetric differential operators |
| title_full_unstemmed | Galois orders of symmetric differential operators |
| title_short | Galois orders of symmetric differential operators |
| title_sort | galois orders of symmetric differential operators |
| topic | Weyl algebra invariant differential operators Galois order filed of fractions 13N10 16D30 16S32 16S85 |
| topic_facet | Weyl algebra invariant differential operators Galois order filed of fractions 13N10 16D30 16S32 16S85 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/442 |
| work_keys_str_mv | AT futornyvyacheslav galoisordersofsymmetricdifferentialoperators AT schwarzjoao galoisordersofsymmetricdifferentialoperators |