Compactly embedded Cartan algebras and invariant cones in Lie algebras

DOI10.1016/0001-8708(89)90036-4zbMath0685.22004OpenAlexW1999658897MaRDI QIDQ1825973

Joachim Hilgert, Karl Heinrich Hofmann

Publication date: 1989

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0001-8708(89)90036-4

zbMATH Keywords

Lie algebrasinvariant conesadjoint representationmaximal toriCartan algebrasclosures of linear Lie groups

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Structure theory for Lie algebras and superalgebras (17B05) Infinite-dimensional Lie (super)algebras (17B65) Lie algebras of Lie groups (22E60) General properties and structure of real Lie groups (22E15) Duality theory for topological vector spaces (46A20) Convex sets in topological vector spaces (aspects of convex geometry) (52A07) Lie algebras of linear algebraic groups (17B45) Ordered abelian groups, Riesz groups, ordered linear spaces (06F20)

Related Items

Holomorphic representation theory. II, Holomorphic representation theory. I, Invariant cones in Lie algebras, Classification of invariant cones in Lie algebras, Invariant cones in solvable Lie algebras, Symmetric spaces of Hermitian type

Cites Work

• Determination of invariant convex cones in simple Lie algebras
• On invariant convex cones in simple Lie algebras
• Lorentzian cones in real Lie algebras
• On the automorphism group of cones and wedges
• Old and new on Sl(2)
• Invariant convex cones and orderings in Lie groups
• Invariant convex cones and causality in semisimple Lie algebras and groups
• Invariant cones in Lie algebras, Lie semigroups, and the holomorphic discrete series
• Semigroups in Lie Groups, Semialgebras in Lie Algebras
• Splitting in topological groups
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