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On Lie algebra obstructions

Published online by Cambridge University Press:  17 April 2009

J. Knopfmacher
J. Knopfmacher
Affiliation:
University of the Witwatersrand, Johannesburg, South Africa.
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Abstract

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A basic problem in the theory of Lie algebra extensions concerns a given homomorphism X of a Lie algebra L into the Lie algebra of outer derivations of a Lie algebra B. In analogy with the theory of group extensions, Mori and HochschiId developed the concept of an obstruction to X being the homomorphism defined by some Lie algebra extension of B by L. This note considers an alternative approach to this theory, which is particularly simple when applied to the problem of realizing arbitrary three-cohomology classes of L as obstructions. The approach is analogous to one for groups, which was given recently by Gruenberg.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 1 , Issue 2 , August 1969 , pp. 281 - 288
Copyright
Copyright © Australian Mathematical Society 1969

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