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...
Збережено в:
| Опубліковано в: : | Algebra and Discrete Mathematics |
|---|---|
| Дата: | 2017 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2017
|
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/155929 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Galois orders of symmetric differential operators / V. Futorny, J. Schwarz // Algebra and Discrete Mathematics. — 2017. — Vol. 23, № 1. — С. 35-46. — Бібліогр.: 41 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-155929 |
|---|---|
| record_format |
dspace |
| spelling |
Futorny, V. Schwarz, J. 2019-06-17T15:32:40Z 2019-06-17T15:32:40Z 2017 Galois orders of symmetric differential operators / V. Futorny, J. Schwarz // Algebra and Discrete Mathematics. — 2017. — Vol. 23, № 1. — С. 35-46. — Бібліогр.: 41 назв. — англ. 1726-3255 2010 MSC:13N10, 16D30, 16S32, 16S85. https://nasplib.isofts.kiev.ua/handle/123456789/155929 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 gln and sln 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. Supported in part by CNPq grant (301320/2013-6) and by Fapesp grant(2014/09310-5) Supported in part by Fapesp grant (2014/25612-1) en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Galois orders of symmetric differential operators Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Galois orders of symmetric differential operators |
| spellingShingle |
Galois orders of symmetric differential operators Futorny, V. Schwarz, J. |
| title_short |
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_sort |
galois orders of symmetric differential operators |
| author |
Futorny, V. Schwarz, J. |
| author_facet |
Futorny, V. Schwarz, J. |
| publishDate |
2017 |
| language |
English |
| container_title |
Algebra and Discrete Mathematics |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| 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 gln and sln 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.
|
| issn |
1726-3255 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/155929 |
| citation_txt |
Galois orders of symmetric differential operators / V. Futorny, J. Schwarz // Algebra and Discrete Mathematics. — 2017. — Vol. 23, № 1. — С. 35-46. — Бібліогр.: 41 назв. — англ. |
| work_keys_str_mv |
AT futornyv galoisordersofsymmetricdifferentialoperators AT schwarzj galoisordersofsymmetricdifferentialoperators |
| first_indexed |
2025-12-01T00:31:05Z |
| last_indexed |
2025-12-01T00:31:05Z |
| _version_ |
1850858913027588096 |