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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| Опубліковано в: : | Український математичний журнал |
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| Дата: | 1992 |
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| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
1992
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| Теми: | |
| Онлайн доступ: | 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 |
| 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| Резюме: | 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 |