On Cohn's embedding of an enveloping algebra into a division ring
In 1961 P. М. Cohn proved that the universal enveloping algebra of any Lie algebra over a field-can be embedded into a division ring. (The Lie algebra is not assumed to be finite dimensional.) Cohn's method is less than direct. We give a more explicit construction. These division rings have rec...
Збережено в:
| Опубліковано в: : | Український математичний журнал |
|---|---|
| Дата: | 1992 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
1992
|
| Теми: | |
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/155304 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | On Cohn's embedding of an enveloping algebra into a division ring / B.A.F. Wehrfritz // Український математичний журнал. — 1992. — Т. 44, № 6. — С. 729–735. — Бібліогр.: 5 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862528830528290816 |
|---|---|
| author | Wehrfritz, B.A.F. |
| author_facet | Wehrfritz, B.A.F. |
| citation_txt | On Cohn's embedding of an enveloping algebra into a division ring / B.A.F. Wehrfritz // Український математичний журнал. — 1992. — Т. 44, № 6. — С. 729–735. — Бібліогр.: 5 назв. — англ. |
| collection | DSpace DC |
| container_title | Український математичний журнал |
| description | In 1961 P. М. Cohn proved that the universal enveloping algebra of any Lie algebra over a field-can be embedded into a division ring. (The Lie algebra is not assumed to be finite dimensional.) Cohn's method is less than direct. We give a more explicit construction. These division rings have recently found uses in the theory of skew linear groups.
Let F be a field, L a Lie F-algebra and U=U(L) the universal enveloping algebra of L. In [1] Cohn constructs an embedding of U into a division ring. Recently there has been interest in this specific division ring in connection with matrix groups and matrix rings [2–4]. Cohn's construction is less than direct and it seemed useful to have a very explicit description of D, at least for the benefit of group theorists.
|
| first_indexed | 2025-11-24T02:42:39Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-155304 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1027-3190 |
| language | English |
| last_indexed | 2025-11-24T02:42:39Z |
| publishDate | 1992 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Wehrfritz, B.A.F. 2019-06-16T15:59:40Z 2019-06-16T15:59:40Z 1992 On Cohn's embedding of an enveloping algebra into a division ring / B.A.F. Wehrfritz // Український математичний журнал. — 1992. — Т. 44, № 6. — С. 729–735. — Бібліогр.: 5 назв. — англ. 1027-3190 https://nasplib.isofts.kiev.ua/handle/123456789/155304 512.54 In 1961 P. М. Cohn proved that the universal enveloping algebra of any Lie algebra over a field-can be embedded into a division ring. (The Lie algebra is not assumed to be finite dimensional.) Cohn's method is less than direct. We give a more explicit construction. These division rings have recently found uses in the theory of skew linear groups. Let F be a field, L a Lie F-algebra and U=U(L) the universal enveloping algebra of L. In [1] Cohn constructs an embedding of U into a division ring. Recently there has been interest in this specific division ring in connection with matrix groups and matrix rings [2–4]. Cohn's construction is less than direct and it seemed useful to have a very explicit description of D, at least for the benefit of group theorists. en Інститут математики НАН України Український математичний журнал Статті On Cohn's embedding of an enveloping algebra into a division ring Про Конове вкладення обгортуючої алгебри в кільце з діленням Article published earlier |
| spellingShingle | On Cohn's embedding of an enveloping algebra into a division ring Wehrfritz, B.A.F. Статті |
| title | On Cohn's embedding of an enveloping algebra into a division ring |
| title_alt | Про Конове вкладення обгортуючої алгебри в кільце з діленням |
| title_full | On Cohn's embedding of an enveloping algebra into a division ring |
| title_fullStr | On Cohn's embedding of an enveloping algebra into a division ring |
| title_full_unstemmed | On Cohn's embedding of an enveloping algebra into a division ring |
| title_short | On Cohn's embedding of an enveloping algebra into a division ring |
| title_sort | on cohn's embedding of an enveloping algebra into a division ring |
| topic | Статті |
| topic_facet | Статті |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/155304 |
| work_keys_str_mv | AT wehrfritzbaf oncohnsembeddingofanenvelopingalgebraintoadivisionring AT wehrfritzbaf prokonovevkladennâobgortuûčoíalgebrivkílʹcezdílennâm |