An embedding theorem for Lie algebras

Authors:
Anetta Bajer and Jon F. Carlson

Journal:
Proc. Amer. Math. Soc. **127** (1999), 3445-3449

MSC (1991):
Primary 16W30; Secondary 17B30, 17B56

DOI:
https://doi.org/10.1090/S0002-9939-99-04865-0

Published electronically:
July 22, 1999

MathSciNet review:
1605919

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we give a sufficient condition for a restricted enveloping algebra to be quasi-elementary. We also prove that every finite dimensional -nilpotent Lie algebra can be embedded in a finite dimensional -nilpotent quasi-elementary Lie algebra.

**1.**J. F. Carlson,*The cohomology ring of a module*, JPAA**36**(1985), 105-121. MR**86f:20062****2.**J. C. Jantzen,*Kohomologie von -Lie-algebren und nilpotente elemente*, Abh. Math. Sem. Univ. Hamburg**56**(1986).MR**88e:17019****3.**John W. Milnor and John C. Moore,*On the structure of Hopf algebras*, Ann. of Math.**81**(1965), 211-264. MR**30:4259****4.**E. Friedlander and B. Parshall,*Cohomology of infinitesimal and discrete groups*, Math. Ann.**273**(1986), 353-374. MR**87e:22026****5.**D. K. Nakano and J. H. Palmieri,*Support varieties for the Steenrod algebra*, Math. Z.**227**(1998), 663-684. CMP**98:12****6.**J. H. Palmieri,*A note on the cohomology of finite dimensional cocommutative Hopf algebras*, J. of Algebra**188**(1997), 203-215. MR**98a:16043****7.**D. Quillen,*The spectrum of an equivariant cohomology ring, I*, Ann. of Math.**94**(1971), 549-572. MR**45:7743****8.**-,*The spectrum of an equivariant cohomology ring, II*, Ann. of Math.**94**(1971), 573-602. MR**45:7743****9.**J. P. Serre,*Sur la dimension cohomologique des groupes profinis*, Topology**3**(1965), 413-420. MR**31:4853**

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Additional Information

**Anetta Bajer**

Affiliation:
Department of Mathematics, Fordham University, Bronx, New York 10458

Email:
bajer@murray.fordham.edu

**Jon F. Carlson**

Affiliation:
Department of Mathematics, University of Georgia, Athens, Georgia 30602

Email:
jfc@sloth.math.uga.edu

DOI:
https://doi.org/10.1090/S0002-9939-99-04865-0

Keywords:
Restricted enveloping algebra,
quasi-elementary Hopf algebra,
$p$-nilpotent Lie algebra

Received by editor(s):
June 28, 1996

Received by editor(s) in revised form:
January 5, 1998

Published electronically:
July 22, 1999

Additional Notes:
The second author was partially supported by a grant from NSF

Communicated by:
Roe Goodman

Article copyright:
© Copyright 1999
American Mathematical Society