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

Author(s): Donald W. Barnes
Journal: Proc. Amer. Math. Soc. 129 (2001), 347-350.
MSC (1991): Primary 18G40, 17B56
Posted: August 29, 2000
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Abstract:

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.

References:

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[2]: -, Sortability of representations of Lie algebras, J. Alg. 27 (1973), 486-490. MR 51:3242
[3]: -, Spectral sequence constructors in algebra and topology, Mem. Amer. Math. Soc. 53 No. 317, 1985. MR 86e:55032
[4]: H. Cartan and S. Eilenberg, Homological algebra, Princeton University Press, 1956. MR 17:1040e
[5]: J. Dixmier, Cohomologie des algèbres de Lie nilpotentes, Acta Sci. Math. Szeged. 16 (1955), 246-250. MR 17:645b


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