Mostow's Decomposition Theorem for L*-groups and Applications to affine coadjoint orbits and stable manifolds
| dc.creator | Tumpach, A. B. | |
| dc.date | 2006-05-11 | |
| dc.date.accessioned | 2026-07-07T07:13:44Z | |
| dc.date.available | 2026-07-07T07:13:44Z | |
| dc.description | 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 G^C 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. | |
| dc.description | 17 pages | |
| dc.identifier | https://arxiv.org/abs/math-ph/0605039 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0605039 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/112583 | |
| dc.subject | Mathematical Physics | |
| dc.title | Mostow's Decomposition Theorem for L*-groups and Applications to affine coadjoint orbits and stable manifolds | |
| dc.type | text |