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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| Видавець: | Інститут прикладної математики і механіки НАН України |
|---|---|
| Дата: | 2013 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2013
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/152257 |
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| Цитувати: | 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. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-152257 |
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irk-123456789-1522572019-06-10T01:25:51Z Automorphic equivalence of the representations of Lie algebras Shestakov, I. Tsurkov, A. 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. 2013 Article 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 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Shestakov, I. Tsurkov, A. |
| spellingShingle |
Shestakov, I. Tsurkov, A. Automorphic equivalence of the representations of Lie algebras Algebra and Discrete Mathematics |
| author_facet |
Shestakov, I. Tsurkov, A. |
| author_sort |
Shestakov, I. |
| title |
Automorphic equivalence of the representations of Lie algebras |
| title_short |
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_sort |
automorphic equivalence of the representations of lie algebras |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2013 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/152257 |
| 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. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT shestakovi automorphicequivalenceoftherepresentationsofliealgebras AT tsurkova automorphicequivalenceoftherepresentationsofliealgebras |
| first_indexed |
2023-05-20T17:37:52Z |
| last_indexed |
2023-05-20T17:37:52Z |
| _version_ |
1796153731494969344 |