G* Modules

  • Victor W. Guillemin
  • Shlomo Sternberg
  • Jochen Brüning
Chapter

Abstract

Throughout the rest of this monograph we will use a restricted version of the Einstein summation convention: A summation is implied whenever a repeated Latin letter occurs as a superscript and a subscript, but not if the repeated index is a Greek letter. So, for example, if g is a Lie algebra, and we have fixed a basis, ξ 1,...,ξ n we have
$$\left[ {{\xi _i},{\xi _j}} \right] = c_{ij}^k{\xi _k}$$
where the \(c_{ij}^k\) are called the structure constants of g relative to our chosen basis.

Keywords

Manifold Dinate 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Victor W. Guillemin
    • 1
  • Shlomo Sternberg
    • 2
  • Jochen Brüning
    • 3
  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA
  2. 2.Department of MathematicsHarvard UniversityCambridgeUSA
  3. 3.Institut für Mathematik Mathematisch-Naturwissenschaftliche Fakultät IIHumboldt-Universität BerlinBerlinGermany

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