On Strongly Inert Subalgebras of an Infinite-Dimensional Lie Algebra
We study infinite-dimensional Lie algebras L over an arbitrary field that contain a subalgebra A such that dim(A + [A, L])/A < ∞. We prove that if an algebra L is locally finite, then the subalgebra A is contained in a certain ideal I of the Lie algebra L such that dimI/A
Gespeichert in:
| Datum: | 2002 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Russisch Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2002
|
| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/4143 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Institution
Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510278252232704 |
|---|---|
| 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 | 2020-03-18T20:23:13Z |
| description | We study infinite-dimensional Lie algebras L over an arbitrary field that contain a subalgebra A such that dim(A + [A, L])/A < ∞. We prove that if an algebra L is locally finite, then the subalgebra A is contained in a certain ideal I of the Lie algebra L such that dimI/A |
| first_indexed | 2026-03-24T02:54:27Z |
| format | Article |
| fulltext |
0141
0142
0143
0144
|
| id | umjimathkievua-article-4143 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T02:54:27Z |
| publishDate | 2002 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/69/5ca8e6772a8e818ac51a3061d4abf269.pdf |
| spelling | umjimathkievua-article-41432020-03-18T20:23:13Z On Strongly Inert Subalgebras of an Infinite-Dimensional Lie Algebra О сильно инертных подалгебрах бесконечномерной алгебры Ли Petravchuk, A. P. Петравчук, А. П. Петравчук, А. П. We study infinite-dimensional Lie algebras L over an arbitrary field that contain a subalgebra A such that dim(A + [A, L])/A < ∞. We prove that if an algebra L is locally finite, then the subalgebra A is contained in a certain ideal I of the Lie algebra L such that dimI/A Вивчаються нескінченновимірні алгебри Лі $L$ над довільним полем, які містять підалгебру $A$ з властивістю $\dim (A + [A, L])/A < ∞$. Доведено, що у випадку локальної скінченносгі алгебри $L$ підалгебра $A$ міститься в деякому ідеалі $I$ алгебри Лі $L$ такому, що $\dim I/A < ∞$. Показано, що умова локальної скінченносгі алгебри $L$ в цьому твердженні є суттєвою. Institute of Mathematics, NAS of Ukraine 2002-07-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4143 Ukrains’kyi Matematychnyi Zhurnal; Vol. 54 No. 7 (2002); 1025-1028 Український математичний журнал; Том 54 № 7 (2002); 1025-1028 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4143/4995 https://umj.imath.kiev.ua/index.php/umj/article/view/4143/4996 Copyright (c) 2002 Petravchuk A. P. |
| spellingShingle | Petravchuk, A. P. Петравчук, А. П. Петравчук, А. П. On Strongly Inert Subalgebras of an Infinite-Dimensional Lie Algebra |
| title | On Strongly Inert Subalgebras of an Infinite-Dimensional Lie Algebra |
| title_alt | О сильно инертных подалгебрах бесконечномерной алгебры Ли |
| title_full | On Strongly Inert Subalgebras of an Infinite-Dimensional Lie Algebra |
| title_fullStr | On Strongly Inert Subalgebras of an Infinite-Dimensional Lie Algebra |
| title_full_unstemmed | On Strongly Inert Subalgebras of an Infinite-Dimensional Lie Algebra |
| title_short | On Strongly Inert Subalgebras of an Infinite-Dimensional Lie Algebra |
| title_sort | on strongly inert subalgebras of an infinite-dimensional lie algebra |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4143 |
| work_keys_str_mv | AT petravchukap onstronglyinertsubalgebrasofaninfinitedimensionalliealgebra AT petravčukap onstronglyinertsubalgebrasofaninfinitedimensionalliealgebra AT petravčukap onstronglyinertsubalgebrasofaninfinitedimensionalliealgebra AT petravchukap osilʹnoinertnyhpodalgebrahbeskonečnomernojalgebryli AT petravčukap osilʹnoinertnyhpodalgebrahbeskonečnomernojalgebryli AT petravčukap osilʹnoinertnyhpodalgebrahbeskonečnomernojalgebryli |