On ideals in

  • Ivan Penkov

    Jacobs-Universität Bremen, Germany
  • Alexey Petukhov

    The University of Manchester, UK
On ideals in $\operatorname{U}(\mathfrak {sl} (\infty)), \operatorname{U}(\mathfrak {o} (\infty)), \operatorname{U}(\mathfrak {sp} (\infty))$ cover
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We provide a review of results on two-sided ideals in the enveloping algebra of a locally simple Lie algebra . We pay special attention to the case when is one of the finitary Lie algebras . The main results include a description of all integrable ideals in , as well as a criterion for the annihilator of an arbitrary (not necessarily integrable) simple highest weight module to be nonzero. This criterion is new for . All annihilators of simple highest weight modules are integrable ideals for . Finally, we prove that the lattices of ideals in and are isomorphic.