Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-20T15:23:10.348Z Has data issue: false hasContentIssue false
  • English
  • Français

Finitely sorting 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:
Department of Pure Mathematics University of SydneyN.S.W. 2006, Australia
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Lie algebras whose finite-dimensional modules decompose into direct sums of modules involving only one type of irreducible are investigated. Some vanishing theorems for the cohomology of some infinite-dimensional Lie algebras are thereby obtained.

Keywords

Lie algebrascohomology

MSC classification

Secondary: 17B56: Cohomology of Lie (super)algebras 17B55: Homological methods in Lie (super)algebras
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 49 , Issue 3 , December 1990 , pp. 354 - 363
Copyright
Copyright © Australian Mathematical Society 1990

References

[1]Barnes, D. W., ‘Sortability of representations of Lie algebras’, J. Algebra 27 (1973), 486–490.CrossRefGoogle Scholar
[2]Farnsteiner, R., ‘On the vanishing of homology and cohomology groups of associative algebras’, Trans. Amer. Math. Soc. 306 (1988), 651–665.CrossRefGoogle Scholar
[3]Jacobson, N., Lie algebras, Interscience Tracts in Pure and Appl. Math., (John Wiley & Sons, New York and London, 1962).Google Scholar
[4]Magnus, W., Karrass, A. and Solitar, D., Combinatorial group theory, (Interscience-Wiley, New York, London, Sydney, 1966).Google Scholar
[5]Mitra, B., Sitaram, B. R. and Tripathy, K. C., ‘Cohomology of Lie algebras with a nontrivial center’, J. Math. Phys. 25 (1984), 443–444.CrossRefGoogle Scholar
[6]Serre, J-P., Algèbres de Lie semi-simples complexes, Benjamin, New York and Amsterdam, 1966.Google Scholar