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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 \(\left(k\right) =0.\) We consider the representations of Lie algebras as \(2\)-sorted universal algebras. The representations of groups were...
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Lugansk National Taras Shevchenko University
2018
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oai:ojs.admjournal.luguniv.edu.ua:article-7372018-04-26T00:47:27Z Automorphic equivalence of the representations of Lie algebras Shestakov, I. Tsurkov, A. universal algebraic geometry, representations of Lie algebras, automorphic equivalence 17B10 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 \(\left(k\right) =0.\) 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. Lugansk National Taras Shevchenko University 2018-04-26 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/737 Algebra and Discrete Mathematics; Vol 15, No 1 (2013) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/737/268 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| collection |
OJS |
| language |
English |
| topic |
universal algebraic geometry representations of Lie algebras automorphic equivalence 17B10 |
| spellingShingle |
universal algebraic geometry representations of Lie algebras automorphic equivalence 17B10 Shestakov, I. Tsurkov, A. Automorphic equivalence of the representations of Lie algebras |
| topic_facet |
universal algebraic geometry representations of Lie algebras automorphic equivalence 17B10 |
| format |
Article |
| author |
Shestakov, I. Tsurkov, A. |
| 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 |
| 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 \(\left(k\right) =0.\) 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. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/737 |
| work_keys_str_mv |
AT shestakovi automorphicequivalenceoftherepresentationsofliealgebras AT tsurkova automorphicequivalenceoftherepresentationsofliealgebras |
| first_indexed |
2024-04-12T06:26:52Z |
| last_indexed |
2024-04-12T06:26:52Z |
| _version_ |
1796109198906359808 |