1999/09/01 by Sam Evens, Jiang-Hua Lu, Evens, Sam +1
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.DG
paper · pdf · doi:10.48550/arxiv.math/9909005
arxiv created 1999/09/01 · openalex publication_date 1999/09/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study Lagrangian subalgebras of a semisimple Lie algebra with respect to the imaginary part of the Killing form. We show that the variety \Lagr of Lagrangian subalgebras carries a natural Poisson structure Π. We determine the irreducible components of \Lagr, and we show that each irreducible component is a smooth fiber bundle over a generalized flag variety, and that the fiber is the product of the real points of a De Concini-Procesi compactification and a compact homogeneous space. We study some properties of the Poisson structure Π and show that it contains many interesting Poisson submanifolds.