On the sum of two Lie algebras with finite-dimensional commutants
We prove that an infinite-dimensional Lie algebra over an arbitrary field which is decomposable into the sum of two of its subalgebras with finite-dimensional commutants is almost solvable.
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| Date: | 1995 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
1995
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/5505 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511738354466816 |
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| 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 | 2020-03-19T09:12:10Z |
| description | We prove that an infinite-dimensional Lie algebra over an arbitrary field which is decomposable into the sum of two of its subalgebras with finite-dimensional commutants is almost solvable. |
| first_indexed | 2026-03-24T03:17:40Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-5505 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:17:40Z |
| publishDate | 1995 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/0f/d89e45abada4f5df350739659db2c90f.pdf |
| spelling | umjimathkievua-article-55052020-03-19T09:12:10Z On the sum of two Lie algebras with finite-dimensional commutants О сумме двух алгебр Ли с конечномерными коммутантами Petravchuk, A. P. Петравчук, А. П. Петравчук, А. П. We prove that an infinite-dimensional Lie algebra over an arbitrary field which is decomposable into the sum of two of its subalgebras with finite-dimensional commutants is almost solvable. Доведено, що нескінченновимірна алгебра Лi над довільним полем, яка розкладається в суму двох своїх підалгебр із скінченновимірними комутантами, майже розв'язна. Institute of Mathematics, NAS of Ukraine 1995-08-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5505 Ukrains’kyi Matematychnyi Zhurnal; Vol. 47 No. 8 (1995); 1089–1096 Український математичний журнал; Том 47 № 8 (1995); 1089–1096 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/5505/7699 https://umj.imath.kiev.ua/index.php/umj/article/view/5505/7700 Copyright (c) 1995 Petravchuk A. P. |
| spellingShingle | Petravchuk, A. P. Петравчук, А. П. Петравчук, А. П. On the sum of two Lie algebras with finite-dimensional commutants |
| title | On the sum of two Lie algebras with finite-dimensional commutants |
| title_alt | О сумме двух алгебр Ли с конечномерными коммутантами |
| title_full | On the sum of two Lie algebras with finite-dimensional commutants |
| title_fullStr | On the sum of two Lie algebras with finite-dimensional commutants |
| title_full_unstemmed | On the sum of two Lie algebras with finite-dimensional commutants |
| title_short | On the sum of two Lie algebras with finite-dimensional commutants |
| title_sort | on the sum of two lie algebras with finite-dimensional commutants |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5505 |
| work_keys_str_mv | AT petravchukap onthesumoftwoliealgebraswithfinitedimensionalcommutants AT petravčukap onthesumoftwoliealgebraswithfinitedimensionalcommutants AT petravčukap onthesumoftwoliealgebraswithfinitedimensionalcommutants AT petravchukap osummedvuhalgebrliskonečnomernymikommutantami AT petravčukap osummedvuhalgebrliskonečnomernymikommutantami AT petravčukap osummedvuhalgebrliskonečnomernymikommutantami |