Automorphic equivalence of the representations of Lie algebras
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...
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| Published in: | Algebra and Discrete Mathematics |
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| Date: | 2013 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2013
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/152257 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862631040538902528 |
|---|---|
| author | Shestakov, I. Tsurkov, A. |
| author_facet | Shestakov, I. Tsurkov, A. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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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| first_indexed | 2025-11-30T11:09:43Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-152257 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-11-30T11:09:43Z |
| publishDate | 2013 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Shestakov, I. Tsurkov, A. 2019-06-09T13:36:43Z 2019-06-09T13:36:43Z 2013 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. https://nasplib.isofts.kiev.ua/handle/123456789/152257 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. We acknowledge the support by FAPESP - Fundação de Amparo à Pesquisa do Estado de São Paulo (Foundation for Support Research of the State São Paulo), projects No. 2010/50948-2 and No. 2010/50347-9. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Automorphic equivalence of the representations of Lie algebras Article published earlier |
| spellingShingle | Automorphic equivalence of the representations of Lie algebras Shestakov, I. Tsurkov, A. |
| title | Automorphic equivalence of the representations of Lie algebras |
| title_full | Automorphic equivalence of the representations of Lie algebras |
| title_fullStr | Automorphic equivalence of the representations of Lie algebras |
| title_full_unstemmed | Automorphic equivalence of the representations of Lie algebras |
| title_short | Automorphic equivalence of the representations of Lie algebras |
| title_sort | automorphic equivalence of the representations of lie algebras |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/152257 |
| work_keys_str_mv | AT shestakovi automorphicequivalenceoftherepresentationsofliealgebras AT tsurkova automorphicequivalenceoftherepresentationsofliealgebras |