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Constructing Groups Associated to Infinite-Dimensional Lie Algebras

  • Victor G. Kac
Part of the Mathematical Sciences Research Institute Publications book series (MSRI, volume 4)

Abstract

In these notes a representation theoretical approach to the construction of groups associated to (possibly infinite-dimensional) “integrable” Lie algebras is discussed. In the first part a general framework is outlined; here most of the discussion consists of definitions, examples and open problems. Deep results are available only in the case of groups associated to Kac-Moody algebras, which are discussed in the second part; it is based on joint work with Dale Peterson [18], [19], [20], [21], [22], [26]. Extension of these results to other classes of groups, like the group of biregular automorphisms of an affine space, would provide a solution to some very difficult open problems of algebraic geometry.

Keywords

Exact Sequence Weyl Group Regular Function Bruhat Order Flag 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 1985

Authors and Affiliations

  • Victor G. Kac
    • 1
  1. 1.Department of MathematicsMITCambridgeUSA

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