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An Introduction to Affine Kac Moody Lie Algebras and Groups

  • Shrawan Kumar
Chapter
Part of the Progress in Mathematics book series (PM, volume 204)

Abstract

The collection of indecomposable Kac-Moody algebras is divided into three mutually exclusive types: finite, affine, and indefinite. The finite type indecomposable Kac-Moody algebras are precisely the finite-dimensional simple Lie algebras. The aim of this chapter is to explicitly realize the Kac-Moody algebras of affine type (also called the affine Kac-Moody algebras) and the associated groups. Most of the important applications of Kac-Moody theory so far center around this type. Actually, we only consider the Kac-Moody algebras g and the associated groups G of “untwisted” affine type. The “twisted” ones are obtained from the untwisted g as the subalgebra consisting of the elements fixed under an automorphism of g of finite order. The twisted affine Kac-Moody groups are obtained similarly.

Keywords

Algebraic Group Weyl Group Parabolic Subgroup Root Vector Schubert Variety 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • Shrawan Kumar
    • 1
  1. 1.Department of MathematicsUniversity of North Carolina, Chapel HillChapel HillUSA

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