Prime ideals of the enveloping algebra U(sl₃)

Abstract

All prime ideals of the enveloping algebra U= U(sl ₃), over an arbitrary field of characteristic zero, are listed by generators and classified by height. The inclusions between these ideals are also determined. Each prime ideal Iof Uis presented by generators in several different ways. At one pole, we give a generating set for Ias an adjoint module, and this includes a description for the expression of every possible highest weight element of I. At the other pole, except for the case when the ideal is generated by the central variablesIhas a single generator as a two-sided ideal of U.

Keywords:

• Enveloping algebra
• prime ideal
• primitive ideal
• adjoint module
• isotypical component
• highest weight vector