Primitive ideals of U(sl(∞))

We provide an explicit description of the primitive ideals of the enveloping algebra U(sl()) of the infinite-dimensional finitary Lie algebra sl() over an uncountable algebraically closed field of characteristic 0. Our main new result is that any primitive ideal of U(sl()) is integrable. A classification of integrable primitive ideals has been known previously, and relies on the pioneering work of Zhilinskii. We also present an inclusion criterion for primitive ideals of U(sl()).