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...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Український математичний журнал
Datum:1992
1. Verfasser: Wehrfritz, B.A.F.
Format: Artikel
Sprache:English
Veröffentlicht: Інститут математики НАН України 1992
Schlagworte:
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/155304
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
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.

Institution

Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-155304
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
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.
issn 1027-3190
url https://nasplib.isofts.kiev.ua/handle/123456789/155304
fulltext 0005-2 0006 0007 0008 0009 0010 0011-k
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.
work_keys_str_mv AT wehrfritzbaf oncohnsembeddingofanenvelopingalgebraintoadivisionring
AT wehrfritzbaf prokonovevkladennâobgortuûčoíalgebrivkílʹcezdílennâm
first_indexed 2025-11-24T02:42:39Z
last_indexed 2025-11-24T02:42:39Z
_version_ 1850837004809404416