2006/05/11 by Alice Barbara Tumpach, A. B. Tumpach, Tumpach, A. B. · 2 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #FOS: Physical sciences #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.math-ph/0605039
17 pages
arxiv created 2006/05/11 · openalex publication_date 2006/05/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Mostow's Decomposition Theorem is a refinement of the polar decomposition. It states the following. Let G be a compact connected semi-simple Lie group with Lie algebra g. Given a subspace h of g such that [X, [X, Y]] belongs to h for all X and Y in h, the complexified group GC with Lie algebra g + ig is homeomorphic to the product G .exp im. exp ih, where m is the orthogonal of h in g with respect to the Killing form. This Theorem is related to geometric properties of the non-positively curved space of positive-definite symmetric matrices and to a characterization of its geodesic subspaces. The original proof of this Theorem given by Mostow uses the compactness of G. We give a proof of this Theorem using the completeness of the Lie algebra g instead, which can therefore be applied to an L*-group of arbitrary dimension. Some applications of this Theorem to the geometry of stable manifolds and affine coadjoint orbits are given.