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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| Published in: | Algebra and Discrete Mathematics |
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| Date: | 2017 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2017
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/155929 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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| Summary: | 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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| ISSN: | 1726-3255 |