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Extensions of Lie Algebras andthe Third Cohomology Group

Published online by Cambridge University Press:  20 November 2018

S. I. Goldberg
S. I. Goldberg*
Affiliation:
Lehigh University
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Cohomology theories of various algebraic structures have been investigated by several authors. The most noteworthy are due to Hochschild, MacLane and Eckmann, Chevalley and Eilenberg, who developed the theory of cohomology groups of associative algebras, abstract groups, and Lie algebras respectively. In this paper we are concerned primarily with a characterization of the third cohomology group of a Lie algebra by its extension properties.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 5 , 1953 , pp. 470 - 476
Copyright
Copyright © Canadian Mathematical Society 1953

References

1. Chevalley, C., Theory of Lie groups (Princeton, 1946).Google Scholar
2. Chevalley, C. and Eilenberg, S., Cohomology theory of Lie groups and Lie algebras, Trans. Amer. Math. Soc, 63 (1948), 85–124.Google Scholar
3. Eilenberg, S. and MacLane, S., Cohomology and Galois theory I: Normality of algebras and Teichmiiller's cocycle, Trans. Amer. Math. Soc, 64 (1948), 1–20.Google Scholar
4. Teichmiiller, O., Über die sogenannte nichtkommutative Galoissche Theorie und die Relation , Dtsch. Math., 5 (1940), 138–149.Google Scholar