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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| Veröffentlicht in: | Algebra and Discrete Mathematics |
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| Datum: | 2017 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут прикладної математики і механіки НАН України
2017
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/155929 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862639118259847168 |
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| author | Futorny, V. Schwarz, J. |
| author_facet | Futorny, V. Schwarz, J. |
| 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. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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.
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| first_indexed | 2025-12-01T00:31:05Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-155929 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-01T00:31:05Z |
| publishDate | 2017 |
| publisher | Інститут прикладної математики і механіки НАН України |
| 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 |
| spellingShingle | Galois orders of symmetric differential operators Futorny, V. Schwarz, J. |
| 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/155929 |
| work_keys_str_mv | AT futornyv galoisordersofsymmetricdifferentialoperators AT schwarzj galoisordersofsymmetricdifferentialoperators |