Properness of Lie algebras and enveloping algebras. I

Michaelis, Walter

doi:10.1090/S0002-9939-1987-0897064-1

Properness of Lie algebras and enveloping algebras. I
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Proc. Amer. Math. Soc. 101 (1987), 17-23 Request permission

Abstract:

An associative unitary (respectively, Lie) algebra is said to be proper in case the intersection of ail of its cofinite two-sided (respectively, Lie) ideals is zero. Using the Hopf algebra structure of $UL$, it is shown that over a field of characteristic zero a Lie algebra is proper if and only if its universal enveloping algebra is proper. (In the finite-dimensional case this provides a new proof of a result of Harish-Chandra.) The analogous result for Lie $p$-algebras and their restricted universal enveloping algebras holds and is proved by the same technique.

References

Lie groups and Lie algebras

Hyperalgèbres et groupes de Lie formels

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