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The aim is to explore the duality between invariant sets and functions in infinite-dimensional Lie algebras and its applications.

March 29, 2026Journal of Lie theoryOpen Access

A Survey on Invariant Cones inInfinite Dimensional Lie Algebras

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The aim is to explore the duality between invariant sets and functions in infinite-dimensional Lie algebras and its applications.
Discussed duality between weak-* closed convex sets and convex functions in the dual space.
Analyzed applications of root decompositions related to elliptic Cartan subalgebras.
Explored classes of infinite Lie algebras, including completions of locally finite Lie algebras.
Established connections between invariant subsets and convexity properties of coadjoint orbits.
Demonstrated that root decompositions are useful for studying various infinite Lie algebras.
Outlined several open problems related to the duality and its applications.

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This survey examines duality between invariant subsets and functions in infinite-dimensional Lie algebras, highlighting its implications.

K.-H. Neeb (2020) studied this question.

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