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 ( ∞ ) ) .