Automorphic equivalence of the representations of Lie algebras
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Automorphic equivalence of the representations of Lie algebras
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| Creator |
Shestakov, I.
Tsurkov, A. |
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| Description |
In this paper we research the algebraic geometry of the representations of Lie algebras over fixed field k. We assume that this field is infinite and char (k) = 0. We consider the representations of Lie algebras as 2-sorted universal algebras. The representations of groups were considered by similar approach: as 2-sorted universal algebras - in [3] and [2]. The basic notions of the algebraic geometry of representations of Lie algebras we define similar to the basic notions of the algebraic geometry of representations of groups (see [2]). We prove that if a field k has not nontrivial automorphisms then automorphic equivalence of representations of Lie algebras coincide with geometric equivalence. This result is similar to the result of [4], which was achieved for representations of groups. But we achieve our result by another method: by consideration of 1-sorted objects. We suppose that our method can be more perspective in the further researches.
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| Date |
2019-06-09T13:36:43Z
2019-06-09T13:36:43Z 2013 |
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| Type |
Article
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| Identifier |
Automorphic equivalence of the representations of Lie algebras / I. Shestakov, A. Tsurkov // Algebra and Discrete Mathematics. — 2013. — Vol. 15, № 1. — С. 96–126. — Бібліогр.: 5 назв. — англ.
1726-3255 2010 MSC:17B10. http://dspace.nbuv.gov.ua/handle/123456789/152257 |
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| Language |
en
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| Relation |
Algebra and Discrete Mathematics
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| Publisher |
Інститут прикладної математики і механіки НАН України
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