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...
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| Дата: | 1992 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
1992
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| Назва видання: | Український математичний журнал |
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| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/155304 |
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| 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. |
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irk-123456789-1553042019-06-17T01:29:09Z On Cohn's embedding of an enveloping algebra into a division ring Wehrfritz, B.A.F. Статті 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. 1992 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/155304 512.54 en Український математичний журнал Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| topic |
Статті Статті |
| spellingShingle |
Статті Статті Wehrfritz, B.A.F. On Cohn's embedding of an enveloping algebra into a division ring 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. |
| format |
Article |
| author |
Wehrfritz, B.A.F. |
| author_facet |
Wehrfritz, B.A.F. |
| author_sort |
Wehrfritz, B.A.F. |
| title |
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_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_sort |
on cohn's embedding of an enveloping algebra into a division ring |
| publisher |
Інститут математики НАН України |
| publishDate |
1992 |
| topic_facet |
Статті |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/155304 |
| 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. |
| series |
Український математичний журнал |
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AT wehrfritzbaf oncohnsembeddingofanenvelopingalgebraintoadivisionring |
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2023-05-20T17:46:34Z |
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2023-05-20T17:46:34Z |
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1796154065034412032 |