ON THE PRIME SPECTRUM OF THE ENVELOPING ALGEBRA AND CHARACTERISTIC VARIETIES

摘要

Let g be a semisimple Lie algebra and U(??), its enveloping algebra. A problem in the theory of non-commutative algebras is the description of the set Spec U(??) of prime ideals in U(??) as topological space. Using the notion of the characteristic variety as introduced by Joseph, we compute some order relations between prime ideals.