Primitive ideals of $U(\mathfrak{sl}(\infty ))$

Abstract

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

Theorem 3.2 is replaced by Appendix in the last version

Cited by in corpus (1)

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