On the sum of an almost abelian Lie algebra and a Lie algebra finite-dimensional over its center
We consider a Lie algebraL over an arbitrary field that is decomposable into the sumL=A+B of an almost Abelian subalgebraA and a subalgebraB finite-dimensional over its center. We prove that this algebra is almost solvable, i.e., it contains a solvable ideal of finite codimension. In particular, the...
Збережено в:
| Дата: | 1999 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Російська Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
1999
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/4650 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510805948104704 |
|---|---|
| author | Petravchuk, A. P. Петравчук, А. П. Петравчук, А. П. |
| author_facet | Petravchuk, A. P. Петравчук, А. П. Петравчук, А. П. |
| author_sort | Petravchuk, A. P. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:10:38Z |
| description | We consider a Lie algebraL over an arbitrary field that is decomposable into the sumL=A+B of an almost Abelian subalgebraA and a subalgebraB finite-dimensional over its center. We prove that this algebra is almost solvable, i.e., it contains a solvable ideal of finite codimension. In particular, the sum of the Abelian and almost Abelian Lie algebras is an almost solvable Lie algebra. |
| first_indexed | 2026-03-24T03:02:51Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-4650 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:02:51Z |
| publishDate | 1999 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/5b/26933dda037a080f9adc80a75c18b65b.pdf |
| spelling | umjimathkievua-article-46502020-03-18T21:10:38Z On the sum of an almost abelian Lie algebra and a Lie algebra finite-dimensional over its center О сумме почти абелевой алгебры Ли и алгебры Ли, конечномерной над своимцешром Petravchuk, A. P. Петравчук, А. П. Петравчук, А. П. We consider a Lie algebraL over an arbitrary field that is decomposable into the sumL=A+B of an almost Abelian subalgebraA and a subalgebraB finite-dimensional over its center. We prove that this algebra is almost solvable, i.e., it contains a solvable ideal of finite codimension. In particular, the sum of the Abelian and almost Abelian Lie algebras is an almost solvable Lie algebra. Доведено, що алгебра Лі $L$ над довільним полем, що розкладається в суму $L = А + В$ майже абелевої підалгебри $A$ і скінчеінновимірної над своїм центром підалгебри 5, майже розв'язна, тобто містить розв'язний ідеал скінченної ковимірпості. Зокрема, сума абелевої та майже абелевої алгебр Лі є майже розв'язною алгеброю Лі. Institute of Mathematics, NAS of Ukraine 1999-05-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4650 Ukrains’kyi Matematychnyi Zhurnal; Vol. 51 No. 5 (1999); 636–644 Український математичний журнал; Том 51 № 5 (1999); 636–644 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4650/6002 https://umj.imath.kiev.ua/index.php/umj/article/view/4650/6003 Copyright (c) 1999 Petravchuk A. P. |
| spellingShingle | Petravchuk, A. P. Петравчук, А. П. Петравчук, А. П. On the sum of an almost abelian Lie algebra and a Lie algebra finite-dimensional over its center |
| title | On the sum of an almost abelian Lie algebra and a Lie algebra finite-dimensional over its center |
| title_alt | О сумме почти абелевой алгебры Ли и алгебры Ли, конечномерной
над своимцешром |
| title_full | On the sum of an almost abelian Lie algebra and a Lie algebra finite-dimensional over its center |
| title_fullStr | On the sum of an almost abelian Lie algebra and a Lie algebra finite-dimensional over its center |
| title_full_unstemmed | On the sum of an almost abelian Lie algebra and a Lie algebra finite-dimensional over its center |
| title_short | On the sum of an almost abelian Lie algebra and a Lie algebra finite-dimensional over its center |
| title_sort | on the sum of an almost abelian lie algebra and a lie algebra finite-dimensional over its center |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4650 |
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