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On -hyperexcentric modules for Lie algebras

Part of: Lie algebras and Lie superalgebras

Published online by Cambridge University Press:  09 April 2009

Donald W. Barnes
Donald W. Barnes
Affiliation:
1 Little Wonga Rd. Cremorne NSW 2090Australia e-mail: donb@netspace.net.au
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Abstract

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Let be a saturated formation of soluble Lie algebras over the field F, and let L ∈ . Let V and W be -hypercentral and -hyperexcentric L-modules respectively. Then V ⊗FW and HomF(V, W) are -hyperexcentric and Hn(L, W) = 0 for all n.

Keywords

Soluble Lie algebrascohomology.

MSC classification

Secondary: 17B30: Solvable, nilpotent (super)algebras 17B56: Cohomology of Lie (super)algebras 17B50: Modular Lie (super)algebras 17B55: Homological methods in Lie (super)algebras
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 74 , Issue 2 , April 2003 , pp. 235 - 238
Copyright
Copyright © Australian Mathematical Society 2003

References

[1]Barnes, D. W., ‘On the cohomology of soluble Lie algebras’, Math. Z. 101 (1967), 343–349.CrossRefGoogle Scholar
[2]Barnes, D. W., ‘On -hypercentral modules for Lie algebras’, Arch. Math. 30 (1978), 1–7.CrossRefGoogle Scholar
[3]Barnes, D. W., ‘Saturated formations of soluble Lie algebras in characteristic 0’, Arch. Math. 30 (1978), 477–480.CrossRefGoogle Scholar
[4]Barnes, D. W. and Gastineau-Hills, H. M., ‘On the theory of soluble Lie algebras’, Math. Z. 106 (1968), 343–354.CrossRefGoogle Scholar