Talk:Dynkin index
Latest comment: 3 years ago by Nkoyi137 in topic Proposal for List improvements
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Proposal for List improvements
editThank you all for contributing to this entry. Here are some suggestions: (1) The Dynkin index is defined for any representation of a simple Lie algebra (there is nothing called "compact Lie algebra"). (2) The notation used $x_\lambda$ is not common in math but might be in some physics book. (3) The Dynkin index is defined for
(3a) a representation,
(3b) a simple subalgebra (up to linear equivalence) of a simple Lie algebra,
(3c) and also for just a simple Lie algebra (as the common divisors of the Dynkin indices of its fundamental representations).
(4) In the definition using the Killing form, it is very important to normalize the trace so that a long root has length square equals to 2. (5) adding refs to the original paper of Dynkin. Nkoyi137 (talk) 15:02, 4 January 2021 (UTC)