Neeb KH (2020)
Publication Type: Journal article, Review article
Publication year: 2020
Book Volume: 30
Pages Range: 513-564
Journal Issue: 2
For the Lie algebra g of a connected infinite-dimensional Lie group G, there is a natural duality between so-called semi-equicontinuous weak-closed convex Ad ∗ (G) -invariant subsets of the dual space g and Ad(G) -invariant lower semicontinuous positively homogeneous convex functions on open convex cones in g. In this survey, we discuss various aspects of this duality and some of its applications to a more systematic understanding of open invariant cones and convexity properties of coadjoint orbits. In particular, we show that root decompositions with respect to elliptic Cartan subalgebras provide powerful tools for important classes of infinite Lie algebras, such as completions of locally finite Lie algebras, Kac-Moody algebras and twisted loop algebras with infinite-dimensional range spaces. We also formulate various open problems.
APA:
Neeb, K.H. (2020). A survey on invariant cones in infinite dimensional lie algebras. Journal of Lie Theory, 30(2), 513-564.
MLA:
Neeb, Karl Hermann. "A survey on invariant cones in infinite dimensional lie algebras." Journal of Lie Theory 30.2 (2020): 513-564.
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