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Invariants of Real Forms of Affine Kac-Moody Lie Algebras

✍ Scribed by Punita Batra

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
217 KB
Volume
223
Category
Article
ISSN
0021-8693

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✦ Synopsis

The theory of Vogan diagrams, which are Dynkin diagrams with an overlay of certain additional information, allows one to give a rapid classification of finitedimensional real semisimple Lie algebras and to make use of this classification in practice. This paper develops a corresponding theory of Vogan diagrams for "almost compact" real forms of indecomposable nontwisted affine Kac-Moody Lie algebras. In this case also, the equivalence classes of Vogan diagrams correspond to the isomorphism classes of almost compact real forms. Although the real forms of such algebras had already been classified, the theory of Vogan diagrams introduces invariants for such algebras and makes it possible to locate a given real form within the classification.

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