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A functorial version of a construction of Hochschild and Mostow for representations of Lie algebras

Published online by Cambridge University Press:  17 April 2009

William H. Wilson
William H. Wilson
Affiliation:
Department of Mathematics, University of Queensland, St Lucia, Queensland.
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Abstract

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Let be a Lie algebra, a complemented ideal of , and W an -module. Hochschild and Mostow have described the construction of a -module “induced” from W, which is finite-dimensional provided W is finite-dimensional and satisfies a nilpotent action condition. This note describes a modification of their construction which is functorial and a weak adjoint to the restriction functor from –modules to -modules.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 18 , Issue 1 , February 1978 , pp. 95 - 98
Copyright
Copyright © Australian Mathematical Society 1978

References

[1]Hochschild, G. and Mostow, G.D., “Extensions of representations of Lie groups and Lie algebras, I”, Amer. J. Math. 79 (1957), 924–942.CrossRefGoogle Scholar
[2]Zassenhaus, Hans, “Über die Darstellungen der Lie-Algebren bei Charakteristik 0”, Comment. Math. Helv. 26 (1952), 252–274.CrossRefGoogle Scholar