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Symplectic convexity theorems and coadjoint orbits
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Towards a Lie theory of locally convex groups
  • K. Neeb
  • Mathematics
  • 17 September 2006
Abstract.In this survey, we report on the state of the art of some of the fundamental problems in the Lie theory of Lie groups modeled on locally convex spaces, such as integrability of Lie algebras,
Structure and Geometry of Lie Groups
Matrix Groups.- Concrete Matrix Groups. The Matrix Exponential Function. Linear Lie Groups. Lie Algebras.- Elementary Structure Theory of Lie Algebras. Root Decomposition. Representation Theory of
A Cartan–Hadamard Theorem for Banach–Finsler Manifolds
In this paper we study Banach–Finsler manifolds endowed with a spray which have seminegative curvature in the sense that the corresponding exponential function has a surjective expansive differential
Lie semigroups and their applications
Lie semigroups and their tangent wedges.- Examples.- Geometry and topology of Lie semigroups.- Ordered homogeneous spaces.- Applications of ordered spaces to Lie semigroups.- Maximal semigroups in
Non-Abelian Extensions of Topological Lie Algebras
  • K. Neeb
  • Mathematics
  • 11 November 2004
ABSTRACT In this article we extend and adapt several results on extensions of Lie algebras to topological Lie algebras over topological fields of characteristic zero. In particular, we describe the
Abelian extensions of infinite-dimensional Lie groups
  • K. Neeb
  • Mathematics
  • 18 February 2004
In the present paper we study abelian extensions of connected Lie groups G modeled on locally convex spaces by smooth G-modules A. We parametrize the extension classes by a suitable cohomology group
Weak Poisson Structures on Infinite Dimensional Manifolds and Hamiltonian Actions
We introduce a notion of a weak Poisson structure on a manifold M modeled on a locally convex space. This is done by specifying a Poisson bracket on a subalgebra \(\mathcal{A}\subseteq C^{\infty
Basic Lie Theory
This chapter is devoted to the subject proper of this book: Lie groups, defined as smooth manifolds with a group structure such that all structure maps (multiplication and inversion) are smooth. Here