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About: Dynkin index     Goto   Sponge   NotDistinct   Permalink

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Type: yago:WikicatLieAlgebrasyago:Abstraction100002137yago:Algebra106012726yago:Cognition100023271yago:Content105809192yago:Discipline105996646yago:KnowledgeDomain105999266yago:Mathematics106000644yago:PsychologicalFeature100023100yago:PureMathematics106003682yago:Science105999797 New Facet based on Instances of this Class

In mathematics, the Dynkin index of a representation with highest weight of a compact simple Lie algebra that has a highest weight is defined by evaluated in the representation . Here are the matrices representing the generators, and is given by evaluated in the defining representation. By taking traces, we find that where the Weyl vector is equal to half of the sum of all the positive roots of . The expression is the value of the quadratic Casimir in the representation . The index is always a positive integer.