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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| Veröffentlicht in: | Український математичний журнал |
|---|---|
| Datum: | 1992 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
1992
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/155304 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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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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 |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
On Cohn's embedding of an enveloping algebra into a division ring |
| spellingShingle |
On Cohn's embedding of an enveloping algebra into a division ring Wehrfritz, B.A.F. Статті |
| 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 |
| author |
Wehrfritz, B.A.F. |
| author_facet |
Wehrfritz, B.A.F. |
| topic |
Статті |
| topic_facet |
Статті |
| publishDate |
1992 |
| language |
English |
| container_title |
Український математичний журнал |
| publisher |
Інститут математики НАН України |
| format |
Article |
| title_alt |
Про Конове вкладення обгортуючої алгебри в кільце з діленням |
| 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.
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| issn |
1027-3190 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/155304 |
| fulltext |
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| 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. |
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AT wehrfritzbaf oncohnsembeddingofanenvelopingalgebraintoadivisionring AT wehrfritzbaf prokonovevkladennâobgortuûčoíalgebrivkílʹcezdílennâm |
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2025-11-24T02:42:39Z |
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2025-11-24T02:42:39Z |
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