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Название: | A Characterization of Derivations and Automorphisms on Some Simple Algebras |
Авторы: | Arzikulov, F. Urinboyev, F. Ergasheva, Sh. |
Дата публикации: | 2022 |
Издатель: | N.N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of Russian Academy of Sciences Ural Federal University named after the first President of Russia B.N. Yeltsin |
Библиографическое описание: | Arzikulov F. A Characterization of Derivations and Automorphisms on Some Simple Algebras / F. Arzikulov, F. Urinboyev, Sh. Ergasheva. — Text : electronic // Ural Mathematical Journal. — 2022. — Volume 8. — № 1. — P. 46-58. |
Аннотация: | In the present paper, we study simple algebras, which do not belong to the well-known classes of algebras (associative algebras, alternative algebras, Lie algebras, Jordan algebras, etc.). The simple finite-dimensional algebras over a field of characteristic 0 without finite basis of identities, constructed by Kislitsin, are such algebras. In the present paper, we consider two such algebras: the simple seven-dimensional anticommutative algebra and the seven-dimensional central simple commutative algebra . We prove that every local derivation of these algebras and is a derivation, and every 2-local derivation of these algebras and is also a derivation. We also prove that every local automorphism of these algebras and is an automorphism, and every 2-local automorphism of these algebras and is also an automorphism. |
Ключевые слова: | SIMPLE ALGEBRA DERIVATION LOCAL DERIVATION 2-LOCAL DERIVATION AUTOMORPHISM LOCAL AUTOMORPHISM 2-LOCAL AUTOMORPHISM BASIS OF IDENTITIES |
URI: | http://elar.urfu.ru/handle/10995/122270 |
Условия доступа: | Creative Commons Attribution License |
Текст лицензии: | https://creativecommons.org/licenses/by/4.0/ |
Идентификатор РИНЦ: | 50043141 |
ISSN: | 2414-3952 |
DOI: | 10.15826/umj.2022.2.004 |
Источники: | Ural Mathematical Journal. 2022. Volume 8. № 2 |
Располагается в коллекциях: | Ural Mathematical Journal |
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Файл | Описание | Размер | Формат | |
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umj_2022_8_2_005.pdf | 146,73 kB | Adobe PDF | Просмотреть/Открыть |
Лицензия на ресурс: Лицензия Creative Commons