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Symplectic Lie Groups

✍ Scribed by Oliver Baues, Vicente Cortés

Publisher
SociΓ©tΓ© MathΓ©matique de France
Year
2016
Tongue
English
Leaves
102
Series
AstΓ©risque 379
Category
Library
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✦ Synopsis

We develop the structure theory of symplectic Lie groups based on the study of their isotropic normal subgroups. The article consists of three main parts. In the first part we show that every symplectic Lie group admits a sequence of subsequent symplectic reductions to a unique irreducible symplectic Lie group. The second part concerns the symplectic geometry of cotangent symplectic Lie groups and the theory of Lagrangian extensions of flat Lie groups. In the third part of the article we analyze the existence problem for Lagrangian normal subgroups in nilpotent symplectic Lie groups.

✦ Subjects

Mathematics;Applied;Geometry & Topology;History;Infinity;Mathematical Analysis;Matrices;Number Systems;Popular & Elementary;Pure Mathematics;Reference;Research;Study & Teaching;Transformations;Trigonometry;Science & Math;Mathematics;Algebra & Trigonometry;Calculus;Geometry;Statistics;Science & Mathematics;New, Used & Rental Textbooks;Specialty Boutique

πŸ“œ SIMILAR VOLUMES

Symplectic Groups
πŸ“ Symplectic Groups
✍ O. T. O'Meara πŸ“‚ Library πŸ“… 1978 πŸ› American Mathematical Society 🌐 English
Symplectic groups
πŸ“ Symplectic groups
✍ O. T. O'Meara πŸ“‚ Library πŸ“… 1978 πŸ› American Mathematical Society 🌐 English

This volume, the sequel to the author's Lectures on Linear Groups, is the definitive work on the isomorphism theory of symplectic groups over integral domains. Recently discovered geometric methods which are both conceptually simple and powerful in their generality are applied to the symplectic grou