On the length of the spectral sequence of a Lie algebra extension

Author:
Donald W. Barnes

Journal:
Proc. Amer. Math. Soc. **129** (2001), 347-350

MSC (1991):
Primary 18G40, 17B56

Published electronically:
August 29, 2000

MathSciNet review:
1800229

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Abstract | References | Similar Articles | Additional Information

The length of the spectral sequence of a Lie algebra extension is at most the dimension of the quotient algebra. We show that this bound can be attained for arbitrarily large quotient algebras even when the algebra is nilpotent and the extension splits.

**[1]**Donald W. Barnes,*On the cohomology of soluble Lie algebras*, Math. Z.**101**(1967), 343–349. MR**0220784****[2]**D. W. Barnes,*Sortability of representations of Lie algebras*, J. Algebra**27**(1973), 486–490. MR**0366997****[3]**D. W. Barnes,*Spectral sequence constructors in algebra and topology*, Mem. Amer. Math. Soc.**53**(1985), no. 317, viii+174. MR**776177**, 10.1090/memo/0317**[4]**Henri Cartan and Samuel Eilenberg,*Homological algebra*, Princeton University Press, Princeton, N. J., 1956. MR**0077480****[5]**J. Dixmier,*Cohomologie des algèbres de Lie nilpotentes*, Acta Sci. Math. Szeged**16**(1955), 246–250 (French). MR**0074780**

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Additional Information

**Donald W. Barnes**

Affiliation:
1 Little Wonga Road, Cremorne, New South Wales 2090, Australia

Email:
donb@netspace.net.au

DOI:
https://doi.org/10.1090/S0002-9939-00-05761-0

Keywords:
Spectral sequence,
Lie algebras

Received by editor(s):
April 16, 1999

Published electronically:
August 29, 2000

Communicated by:
Dan M. Barbasch

Article copyright:
© Copyright 2000
American Mathematical Society